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Format: 1 Online-Ressource (xvi, 571 Seiten) , Illustrationen

ISBN: 9783030028954

Series Statement: Progress in mathematics volume 327

Note: Auf dem Cover: "Ferran Sunyer i Balaguer Award winning monograph"

Additional Edition: Erscheint auch als Druck-Ausgabe ISBN 978-3-030-02894-7

Language: English

Subjects: Mathematics

Keywords: Lie-Gruppe ; Hardy-Ungleichung ; Homogener Raum

DOI: 10.1007/978-3-030-02895-4

URL: Volltext  (kostenfrei)

URL: Volltext  (kostenfrei)

Author information: Ruzhansky, Michael 1972-

UID:

Format: 1 online resource (XVI, 571 p. 1 illus.)

Edition: 1st ed. 2019.

ISBN: 3-030-02895-X

Series Statement: Progress in Mathematics, 327

Content: This open access book provides an extensive treatment of Hardy inequalities and closely related topics from the point of view of Folland and Stein's homogeneous (Lie) groups. The place where Hardy inequalities and homogeneous groups meet is a beautiful area of mathematics with links to many other subjects. While describing the general theory of Hardy, Rellich, Caffarelli-Kohn-Nirenberg, Sobolev, and other inequalities in the setting of general homogeneous groups, the authors pay particular attention to the special class of stratified groups. In this environment, the theory of Hardy inequalities becomes intricately intertwined with the properties of sub-Laplacians and subelliptic partial differential equations. These topics constitute the core of this book and they are complemented by additional, closely related topics such as uncertainty principles, function spaces on homogeneous groups, the potential theory for stratified groups, and the potential theory for general Hörmander's sums of squares and their fundamental solutions. This monograph is the winner of the 2018 Ferran Sunyer i Balaguer Prize, a prestigious award for books of expository nature presenting the latest developments in an active area of research in mathematics. As can be attested as the winner of such an award, it is a vital contribution to literature of analysis not only because it presents a detailed account of the recent developments in the field, but also because the book is accessible to anyone with a basic level of understanding of analysis. Undergraduate and graduate students as well as researchers from any field of mathematical and physical sciences related to analysis involving functional inequalities or analysis of homogeneous groups will find the text beneficial to deepen their understanding.

Note: Introduction -- Analysis on Homogeneous Groups -- Hardy Inequalities on Homogeneous Groups -- Rellich, Caarelli-Kohn-Nirenberg, and Sobolev Type Inequalities -- Fractional Hardy Inequalities -- Integral Hardy Inequalities on Homogeneous Groups -- Horizontal Inequalities on Stratied Groups -- Hardy-Rellich Inequalities and Fundamental Solutions -- Geometric Hardy Inequalities on Stratied Groups -- Uncertainty Relations on Homogeneous Groups -- Function Spaces on Homogeneous Groups -- Elements of Potential Theory on Stratified Groups -- Hardy and Rellich Inequalities for Sums of Squares -- Bibliography -- Index. , English

Additional Edition: ISBN 3-030-02894-1

Language: English

DOI: 10.1007/978-3-030-02895-4

UID:

Format: 1 Online-Ressource (571 p.)

ISBN: 9783030028954

Series Statement: Progress in Mathematics

Content: This open access book provides an extensive treatment of Hardy inequalities and closely related topics from the point of view of Folland and Stein's homogeneous (Lie) groups. The place where Hardy inequalities and homogeneous groups meet is a beautiful area of mathematics with links to many other subjects. While describing the general theory of Hardy, Rellich, Caffarelli-Kohn-Nirenberg, Sobolev, and other inequalities in the setting of general homogeneous groups, the authors pay particular attention to the special class of stratified groups. In this environment, the theory of Hardy inequalities becomes intricately intertwined with the properties of sub-Laplacians and subelliptic partial differential equations. These topics constitute the core of this book and they are complemented by additional, closely related topics such as uncertainty principles, function spaces on homogeneous groups, the potential theory for stratified groups, and the potential theory for general Hörmander's sums of squares and their fundamental solutions. This monograph is the winner of the 2018 Ferran Sunyer i Balaguer Prize, a prestigious award for books of expository nature presenting the latest developments in an active area of research in mathematics. As can be attested as the winner of such an award, it is a vital contribution to literature of analysis not only because it presents a detailed account of the recent developments in the field, but also because the book is accessible to anyone with a basic level of understanding of analysis. Undergraduate and graduate students as well as researchers from any field of mathematical and physical sciences related to analysis involving functional inequalities or analysis of homogeneous groups will find the text beneficial to deepen their understanding

Note: English

Language: English

URL: kostenfrei

UID:

Format: 1 online resource (579 pages)

ISBN: 9783030028954 , 303002895X

Series Statement: Progress in Mathematics Ser. ; v. 327

Content: This open access book provides an extensive treatment of Hardy inequalities and closely related topics from the point of view of Folland and Stein's homogeneous (Lie) groups. The place where Hardy inequalities and homogeneous groups meet is a beautiful area of mathematics with links to many other subjects. While describing the general theory of Hardy, Rellich, Caffarelli-Kohn-Nirenberg, Sobolev, and other inequalities in the setting of general homogeneous groups, the authors pay particular attention to the special class of stratified groups. In this environment, the theory of Hardy inequalities becomes intricately intertwined with the properties of sub-Laplacians and subelliptic partial differential equations. These topics constitute the core of this book and they are complemented by additional, closely related topics such as uncertainty principles, function spaces on homogeneous groups, the potential theory for stratified groups, and the potential theory for general Hörmander's sums of squares and their fundamental solutions. This monograph is the winner of the 2018 Ferran Sunyer i Balaguer Prize, a prestigious award for books of expository nature presenting the latest developments in an active area of research in mathematics. As can be attested as the winner of such an award, it is a vital contribution to literature of analysis not only because it presents a detailed account of the recent developments in the field, but also because the book is accessible to anyone with a basic level of understanding of analysis. Undergraduate and graduate students as well as researchers from any field of mathematical and physical sciences related to analysis involving functional inequalities or analysis of homogeneous groups will find the text beneficial to deepen their understanding.

Note: Introduction -- Analysis on Homogeneous Groups -- Hardy Inequalities on Homogeneous Groups -- Rellich, Caarelli-Kohn-Nirenberg, and Sobolev Type Inequalities -- Fractional Hardy Inequalities -- Integral Hardy Inequalities on Homogeneous Groups -- Horizontal Inequalities on Stratied Groups -- Hardy-Rellich Inequalities and Fundamental Solutions -- Geometric Hardy Inequalities on Stratied Groups -- Uncertainty Relations on Homogeneous Groups -- Function Spaces on Homogeneous Groups -- Elements of Potential Theory on Stratified Groups -- Hardy and Rellich Inequalities for Sums of Squares -- Bibliography -- Index.

Additional Edition: Print version: Ruzhansky, Michael. Hardy Inequalities on Homogeneous Groups : 100 Years of Hardy Inequalities. Cham : Springer Basel AG, ©2019 ISBN 9783030028947

Language: English

URL: ProQuest Ebook Central

UID:

Format: 1 online resource (579 pages)

Edition: 1st ed.

ISBN: 9783030028954

Series Statement: Progress in Mathematics Series v.327

Content: Intro -- Contents -- Preface -- Introduction -- Chapter 1: Analysis on Homogeneous Groups -- Homogeneous groups -- Properties of homogeneous groups -- Homogeneous quasi-norms -- Polar coordinates -- Convolutions -- Polynomials -- Radial and Euler operators -- Radial derivative -- Euler operator -- From radial to non-radial inequalities -- Euler semigroup e-tE*E -- Stratified groups -- Stratified Lie groups -- Extended sub-Laplacians -- Divergence theorem -- Green's identities for sub-Laplacians -- Green's identities for p-sub-Laplacians -- Sub-Laplacians with drift -- Polarizable Carnot groups -- Heisenberg group -- Quaternionic Heisenberg group -- H-type groups -- Chapter 2: Hardy Inequalities on Homogeneous Groups -- Hardy inequalities and sharp remainders -- Hardy inequality and uncertainty principle -- Weighted Hardy inequalities -- Hardy inequalities with super weights -- Hardy inequalities of higher order with super weights -- Two-weight Hardy inequalities -- Critical Hardy inequalities -- Critical Hardy inequalities -- Another type of critical Hardy inequality -- Critical Hardy inequalities of logarithmic type -- Remainder estimates -- Remainder estimates for Lp-weighted Hardy inequalities -- Critical and subcritical Hardy inequalities -- A family of Hardy-Sobolev type inequalities on quasi-balls -- Improved Hardy inequalities on quasi-balls -- Stability of Hardy inequalities -- Stability of Hardy inequalities for radial functions -- Stability of Hardy inequalities for general functions -- Stability of critical Hardy inequality -- Chapter 3: Rellich, Caffarelli-Kohn-Nirenberg, and Sobolev Type Inequalities -- Rellich inequality -- Rellich type inequalities in L2 -- Rellich type inequalities in Lp -- Stability of Rellich type inequalities -- Higher-order Hardy-Rellich inequalities -- Sobolev type inequalities.

Note: Description based on publisher supplied metadata and other sources

Additional Edition: ISBN 9783030028947

Additional Edition: Erscheint auch als Druck-Ausgabe ISBN 9783030028947

Language: English

URL: lizenzpflichtig

UID:

Format: 1 Online-Ressource (XVI, 571 p. 1 illus)

Edition: 1st ed. 2019

ISBN: 9783030028954

Series Statement: Progress in Mathematics 327

Content: Introduction -- Analysis on Homogeneous Groups -- Hardy Inequalities on Homogeneous Groups -- Rellich, Caarelli-Kohn-Nirenberg, and Sobolev Type Inequalities -- Fractional Hardy Inequalities -- Integral Hardy Inequalities on Homogeneous Groups -- Horizontal Inequalities on Stratied Groups -- Hardy-Rellich Inequalities and Fundamental Solutions -- Geometric Hardy Inequalities on Stratied Groups -- Uncertainty Relations on Homogeneous Groups -- Function Spaces on Homogeneous Groups -- Elements of Potential Theory on Stratified Groups -- Hardy and Rellich Inequalities for Sums of Squares -- Bibliography -- Index

Content: This open access book provides an extensive treatment of Hardy inequalities and closely related topics from the point of view of Folland and Stein's homogeneous (Lie) groups. The place where Hardy inequalities and homogeneous groups meet is a beautiful area of mathematics with links to many other subjects. While describing the general theory of Hardy, Rellich, Caffarelli-Kohn-Nirenberg, Sobolev, and other inequalities in the setting of general homogeneous groups, the authors pay particular attention to the special class of stratified groups. In this environment, the theory of Hardy inequalities becomes intricately intertwined with the properties of sub-Laplacians and subelliptic partial differential equations. These topics constitute the core of this book and they are complemented by additional, closely related topics such as uncertainty principles, function spaces on homogeneous groups, the potential theory for stratified groups, and the potential theory for general Hörmander's sums of squares and their fundamental solutions. This monograph is the winner of the 2018 Ferran Sunyer i Balaguer Prize, a prestigious award for books of expository nature presenting the latest developments in an active area of research in mathematics. As can be attested as the winner of such an award, it is a vital contribution to literature of analysis not only because it presents a detailed account of the recent developments in the field, but also because the book is accessible to anyone with a basic level of understanding of analysis. Undergraduate and graduate students as well as researchers from any field of mathematical and physical sciences related to analysis involving functional inequalities or analysis of homogeneous groups will find the text beneficial to deepen their understanding

Additional Edition: ISBN 9783030028947

Additional Edition: Erscheint auch als Druck-Ausgabe ISBN 978-3-030-02894-7

Language: English

DOI: 10.1007/978-3-030-02895-4

URL: kostenfrei

URL: Inhaltstext

UID:

Format: XVI, 571 p. 1 illus. , online resource.

Edition: 1st ed. 2019.

ISBN: 9783030028954

Series Statement: Progress in Mathematics, 327

Content: This open access book provides an extensive treatment of Hardy inequalities and closely related topics from the point of view of Folland and Stein's homogeneous (Lie) groups. The place where Hardy inequalities and homogeneous groups meet is a beautiful area of mathematics with links to many other subjects. While describing the general theory of Hardy, Rellich, Caffarelli-Kohn-Nirenberg, Sobolev, and other inequalities in the setting of general homogeneous groups, the authors pay particular attention to the special class of stratified groups. In this environment, the theory of Hardy inequalities becomes intricately intertwined with the properties of sub-Laplacians and subelliptic partial differential equations. These topics constitute the core of this book and they are complemented by additional, closely related topics such as uncertainty principles, function spaces on homogeneous groups, the potential theory for stratified groups, and the potential theory for general Hörmander's sums of squares and their fundamental solutions. This monograph is the winner of the 2018 Ferran Sunyer i Balaguer Prize, a prestigious award for books of expository nature presenting the latest developments in an active area of research in mathematics. As can be attested as the winner of such an award, it is a vital contribution to literature of analysis not only because it presents a detailed account of the recent developments in the field, but also because the book is accessible to anyone with a basic level of understanding of analysis. Undergraduate and graduate students as well as researchers from any field of mathematical and physical sciences related to analysis involving functional inequalities or analysis of homogeneous groups will find the text beneficial to deepen their understanding.

Note: Introduction -- Analysis on Homogeneous Groups -- Hardy Inequalities on Homogeneous Groups -- Rellich, Caarelli-Kohn-Nirenberg, and Sobolev Type Inequalities -- Fractional Hardy Inequalities -- Integral Hardy Inequalities on Homogeneous Groups -- Horizontal Inequalities on Stratied Groups -- Hardy-Rellich Inequalities and Fundamental Solutions -- Geometric Hardy Inequalities on Stratied Groups -- Uncertainty Relations on Homogeneous Groups -- Function Spaces on Homogeneous Groups -- Elements of Potential Theory on Stratified Groups -- Hardy and Rellich Inequalities for Sums of Squares -- Bibliography -- Index.

In: Springer eBooks

Additional Edition: Printed edition: ISBN 9783030028947

Additional Edition: Printed edition: ISBN 9783030028961

Language: English

DOI: 10.1007/978-3-030-02895-4

URL: https://doi.org/10.1007/978-3-030-02895-4

UID:

Format: 1 Online-Ressource (xvi, 571 Seiten) : , Illustrationen.

ISBN: 978-3-030-02895-4

Series Statement: Progress in mathematics volume 327

Note: Auf dem Cover: "Ferran Sunyer i Balaguer Award winning monograph"

Additional Edition: Erscheint auch als Druck-Ausgabe ISBN 978-3-030-02894-7

Language: English

Subjects: Mathematics

Keywords: Lie-Gruppe ; Hardy-Ungleichung ; Homogener Raum

DOI: 10.1007/978-3-030-02895-4

URL: Volltext  (kostenfrei)

URL: Volltext  (kostenfrei)

Author information: Ruzhansky, Michael, 1972-,

UID:

Format: xvi, 571 Seiten.

ISBN: 978-3-030-02894-7

Series Statement: Progress in mathematics volume 327

Additional Edition: Erscheint auch als Online-Ausgabe ISBN 978-3-030-02895-4

Language: English

Subjects: Mathematics

Keywords: Lie-Gruppe ; Hardy-Ungleichung ; Homogener Raum

Author information: Ruzhansky, Michael, 1972-,

UID:

Format: 1 online resource (579 pages)

Edition: 1st ed.

ISBN: 9783030028954

Series Statement: Progress in Mathematics Series ; v.327

Note: Intro -- Contents -- Preface -- Introduction -- Chapter 1: Analysis on Homogeneous Groups -- Homogeneous groups -- Properties of homogeneous groups -- Homogeneous quasi-norms -- Polar coordinates -- Convolutions -- Polynomials -- Radial and Euler operators -- Radial derivative -- Euler operator -- From radial to non-radial inequalities -- Euler semigroup e-tE*E -- Stratified groups -- Stratified Lie groups -- Extended sub-Laplacians -- Divergence theorem -- Green's identities for sub-Laplacians -- Green's identities for p-sub-Laplacians -- Sub-Laplacians with drift -- Polarizable Carnot groups -- Heisenberg group -- Quaternionic Heisenberg group -- H-type groups -- Chapter 2: Hardy Inequalities on Homogeneous Groups -- Hardy inequalities and sharp remainders -- Hardy inequality and uncertainty principle -- Weighted Hardy inequalities -- Hardy inequalities with super weights -- Hardy inequalities of higher order with super weights -- Two-weight Hardy inequalities -- Critical Hardy inequalities -- Critical Hardy inequalities -- Another type of critical Hardy inequality -- Critical Hardy inequalities of logarithmic type -- Remainder estimates -- Remainder estimates for Lp-weighted Hardy inequalities -- Critical and subcritical Hardy inequalities -- A family of Hardy-Sobolev type inequalities on quasi-balls -- Improved Hardy inequalities on quasi-balls -- Stability of Hardy inequalities -- Stability of Hardy inequalities for radial functions -- Stability of Hardy inequalities for general functions -- Stability of critical Hardy inequality -- Chapter 3: Rellich, Caffarelli-Kohn-Nirenberg, and Sobolev Type Inequalities -- Rellich inequality -- Rellich type inequalities in L2 -- Rellich type inequalities in Lp -- Stability of Rellich type inequalities -- Higher-order Hardy-Rellich inequalities -- Sobolev type inequalities. , Hardy and Sobolev type inequalities -- Weighted Lp-Sobolev type inequalities -- Stubbe type remainder estimates -- Caffarelli-Kohn-Nirenberg inequalities -- Lp-Caffarelli-Kohn-Nirenberg inequalities -- Higher-order Lp-Caffarelli-Kohn-Nirenberg inequalities -- New type of Lp-Caffarelli-Kohn-Nirenberg inequalities -- Extended Caffarelli-Kohn-Nirenberg inequalities -- Chapter 4: Fractional Hardy Inequalities -- Gagliardo seminorms and fractional p-sub-Laplacians -- Fractional Hardy inequalities on homogeneous groups -- Fractional Sobolev inequalities on homogeneous groups -- Fractional Gagliardo-Nirenberg inequalities -- Fractional Caffarelli-Kohn-Nirenberg inequalities -- Lyapunov inequalities on homogeneous groups -- Lyapunov type inequality for fractional p-sub-Laplacians -- Lyapunov type inequality for systems -- Lyapunov type inequality for Riesz potentials -- Hardy inequalities for fractional sub-Laplacians on stratified groups -- Riesz kernels on stratified Lie groups -- Hardy inequalities for fractional powers of sub-Laplacians -- Landau-Kolmogorov inequalities on stratified groups -- Chapter 5: Integral Hardy Inequalities on Homogeneous Groups -- Two-weight integral Hardy inequalities -- Convolution Hardy inequalities -- Hardy-Littlewood-Sobolev inequalities on homogeneous groups -- Maximal weighted integral Hardy inequality -- Chapter 6: Horizontal Inequalities on Stratified Groups -- Horizontal Lp-Caffarelli-Kohn-Nirenberg inequalities -- Badiale-Tarantello conjecture -- Horizontal higher-order versions -- Horizontal Hardy and Rellich inequalities -- Critical horizontal Hardy type inequality -- Two-parameter Hardy-Rellich inequalities by factorization -- Hardy-Rellich type inequalities and embedding results -- Horizontal Sobolev type inequalities -- Horizontal extended Caffarelli-Kohn-Nirenberg inequalities. , Horizontal Hardy-Rellich type inequalities for p-sub-Laplacians -- Inequalities for weighted p-sub-Laplacians -- Horizontal Rellich inequalities for sub-Laplacians with drift -- Horizontal anisotropic Hardy and Rellich inequalities -- Horizontal Picone identities -- Horizontal anisotropic Hardy type inequality -- Horizontal anisotropic Rellich type inequality -- Horizontal Hardy inequalities with multiple singularities -- Horizontal many-particle Hardy inequality -- Hardy inequality with exponential weights -- Chapter 7: Hardy-Rellich Inequalities and Fundamental Solutions -- Weighted Lp-Hardy inequalities -- Weighted Lp-Rellich inequalities -- Two-weight Hardy inequalities and uncertainty principles -- Rellich inequalities for sub-Laplacians with drift -- Hardy inequalities on the complex affine group -- Hardy inequalities for Baouendi-Grushin operators -- Weighted Lp-inequalities with boundary terms -- Hardy and Caffarelli-Kohn-Nirenberg inequalities -- Rellich inequalities -- Chapter 8: Geometric Hardy Inequalities on Stratified Groups -- L2-Hardy inequality on the half-space -- Examples of Heisenberg and Engel groups -- Lp-Hardy inequality on the half-space -- L2-Hardy inequality on convex domains -- Lp-Hardy inequality on convex domains -- Chapter 9: Uncertainty Relations on Homogeneous Groups -- Abstract position and momentum operators -- Definition and assumptions -- Examples -- Position-momentum relations -- Further position-momentum identities -- Heisenberg-Kennard and Pythagorean inequalities -- Euler-Coulomb relations -- Heisenberg-Pauli-Weyl uncertainty principle -- Radial dilations - Coulomb relations -- Further weighted uncertainty type inequalities -- Chapter 10: Function Spaces on Homogeneous Groups -- Euler-Hilbert-Sobolev spaces -- Poincaré type inequality -- Sobolev-Lorentz-Zygmund spaces -- Generalized Morrey spaces. , Bessel-Riesz kernels on homogeneous groups -- Hardy-Littlewood maximal operator in Morrey spaces -- Bessel-Riesz operators in Morrey spaces -- Generalized Bessel-Riesz operators -- Olsen type inequalities for Bessel-Riesz operator -- Fractional integral operators in Morrey spaces -- Olsen type inequalities for fractional integral operators -- Summary of results -- Besov type space: Gagliardo-Nirenberg inequalities -- Generalized Campanato spaces -- Chapter 11: Elements of Potential Theory on Stratified Groups -- Boundary value problems on stratified groups -- Layer potentials of the sub-Laplacian -- Single layer potentials -- Double layer potential -- Traces and Kac's problem for the sub-Laplacian -- Traces of Newton potential for the sub-Laplacian -- Powers of the sub-Laplacian -- Extended Kohn Laplacians on the Heisenberg group -- Powers of the Kohn Laplacian -- Hardy inequalities with boundary terms on stratified groups -- Green functions on H-type groups -- Green functions and Dirichlet problem in wedge domains -- Green functions and Dirichlet problem in strip domains -- p-sub-Laplacian Picone's inequality and consequences -- Chapter 12: Hardy and Rellich Inequalities for Sums of Squares -- Assumptions -- Examples -- Divergence formula -- Green's identities for sums of squares -- Consequences of Green's identities -- Differential forms, perimeter and surface measures -- Local Hardy inequalities -- Anisotropic Hardy inequalities via Picone identities -- Local uncertainty principles -- Local Rellich inequalities -- Rellich inequalities via Picone identities -- Bibliography -- Index.

Additional Edition: Print version: Ruzhansky, Michael Hardy Inequalities on Homogeneous Groups Cham : Springer International Publishing AG,c2019 ISBN 9783030028947

Language: English

Keywords: Electronic books.

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