Umfang:
Online-Ressource
,
v.: digital
Ausgabe:
Online-Ausg. Springer eBook Collection. Mathematics and Statistics Electronic reproduction; Available via World Wide Web
ISBN:
9783034800723
Serie:
Operator Theory: Advances and Applications 215
Inhalt:
This book provides a systematic development of the Rubio de Francia theory of extrapolation, its many generalizations and its applications to one and two-weight norm inequalities. The book is based upon a new and elementary proof of the classical extrapolation theorem that fully develops the power of the Rubio de Francia iteration algorithm. This technique allows us to give a unified presentation of the theory and to give important generalizations to Banach function spaces and to two-weight inequalities. We provide many applications to the classical operators of harmonic analysis to illustrate our approach, giving new and simpler proofs of known results and proving new theorems. The book is intended for advanced graduate students and researchers in the area of weighted norm inequalities, as well as for mathematicians who want to apply extrapolation to other areas such as partial differential equations.
Anmerkung:
Includes bibliographical references and index -- Includes bibliographical references and indexes
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Weights, Extrapolation and the Theory of Rubio de Francia; Contents; Preface; Preliminaries; Part I One-Weight Extrapolation; Chapter 1 Introduction to Norm Inequalities and Extrapolation; 1.1 Weighted norm inequalities; 1.2 The theory of extrapolation; 1.3 The organization of this book; Chapter 2 The Essential Theorem; 2.1 The new proof; 2.2 Extensions of the extrapolation theorem; Generalized maximal operators; Elimination of the operator; Sharp constants; Off-diagonal extrapolation; Extrapolation for arbitrary pairs of operators; Limited range extrapolation
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Extrapolation to Banach function spacesChapter 3 Extrapolation for Muckenhoupt Bases; 3.1 Preliminaries; Muckenhoupt bases; Pairs of functions; A technical reduction; 3.2 Ap extrapolation; 3.3 Rescaling and extrapolation; A1 extrapolation; 3.4 Sharp extrapolation constants; 3.5 Off-diagonal extrapolation; 3.6 Extrapolation for pairs of positive operators; Extrapolation for one-sided weights; Extrapolation for pairs of positive operators; 3.7 Limited range extrapolation; 3.8 Applications; Norm inequalities for operators; Vector-valued inequalities; Coifman-Fefferman inequalities
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Chapter 4 Extrapolation on Function Spaces4.1 Preliminaries; Banach function spaces; Examples of function spaces; Modular spaces; Examples of modular spaces; 4.2 Extrapolation on Banach function spaces; General function spaces; Rearrangement invariant spaces; 4.3 Extrapolation on modular spaces; 4.4 Applications; Modular spaces and r.i. function spaces; Variable Lebesgue spaces; Part II Two-Weight Factorization and Extrapolation; Chapter 5 Preliminary Results; 5.1 Weights; 5.2 Orlicz spaces; 5.3 Orlicz maximal operators; 5.4 Generalizations of the Ap condition; Log bumps; Log-log bumps
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Exponential log bumpsPower bumps; 5.5 The composition of maximal operators; 5.6 Orlicz fractional maximal operators; 5.7 Composition of fractional maximal operators; Chapter 6 Two-Weight Factorization; 6.1 Reverse factorization and factored weights; 6.2 Factorization of weights; 6.3 Inserting Ap weights; 6.4 Weights for fractional operators; Reverse factorization and factored weights; Factorization of weights; Chapter 7 Two-Weight Extrapolation; 7.1 Two-weight extrapolation; Extrapolation and families of Orlicz bumps; No bump condition; Bp bumps; Log bumps; Exponential log bumps; Power bumps
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7.2 Proof of two-weight extrapolation7.3 Two-weight, weak type extrapolation; 7.4 Extrapolation for factored weights; 7.5 Extrapolation for fractional weights; 7.6 Appendix: A one case proof of extrapolation; Chapter 8 Endpoint and A∞ Extrapolation; 8.1 Endpoint extrapolation; 8.2 Three special cases for the pairs (u,Mu); 8.3 The converse of endpoint extrapolation; 8.4 Endpoint extrapolation for fractional operators; Chapter 9 Applications of Two-Weight Extrapolation; 9.1 The sharp maximal operator; Coifman-Fefferman type inequalities; Proof of Lemma 9.2; 9.2 Singular integral operators
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The conjectures
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Electronic reproduction; Available via World Wide Web
Weitere Ausg.:
ISBN 9783034800716
Sprache:
Englisch
Fachgebiete:
Mathematik
Schlagwort(e):
Extrapolation
DOI:
10.1007/978-3-0348-0072-3
URL:
Volltext
(lizenzpflichtig)
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