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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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