LittlewoodPaley and Multiplier Theory
This book is intended to be a detailed and carefully written account of various versions of the LittlewoodPaley theorem and of some of its applications, together with indications of its general significance in Fourier multiplier theory. We have striven to make the presentation selfcontained and un...
Main Authors:  , 

Corporate Author:  
Format:  eBook 
Language:  English 
Published: 
Berlin, Heidelberg
Springer Berlin Heidelberg
1977, 1977

Edition:  1st ed. 1977 
Series:  Ergebnisse der Mathematik und ihrer Grenzgebiete. 2. Folge, A Series of Modern Surveys in Mathematics

Subjects:  
Online Access:  
Collection:  Springer Book Archives 2004  Collection details see MPG.ReNa 
Table of Contents:
 Prologue
 1. Introduction
 1.1. LittlewoodPaley Theory for T
 1.2. The LP and WM Properties
 1.3. Extension of the LP and R Properties to Product Groups
 1.4 Intersections of Decompositions Having the LP Property
 2. Convolution Operators (ScalarValued Case)
 2.1. Covering Families
 2.2. The Covering Lemma
 2.3. The Decomposition Theorem
 2.4. Bounds for Convolution Operators
 3. Convolution Operators (VectorValued Case)
 3.1. Introduction
 3.2. VectorValued Functions
 3.3. OperatorValued Kernels
 3.4. Fourier Transforms
 3.5. Convolution Operators
 3.6. Bounds for Convolution Operators
 4. The LittlewoodPaley Theorem for Certain Disconnected Groups
 4.1. The LittlewoodPaley Theorem for a Class of Totally Disconnected Groups
 4.2. The LittlewoodPaley Theorem for a More General Class of Disconnected Groups?
 4.3. A LittlewoodPaley Theorem for Decompositions of ? Determined by a Decreasing Sequence of Subgroups
 Historical Notes
 References
 Terminology
 Index of Notation
 Index of Authors and Subjects
 7.5. Fournier’s Example
 8. Strong Forms of the Marcinkiewicz Multiplier Theorem and LittlewoodPaley Theorem for ?, Tand ?
 8.1. Introduction
 8.2. The Strong Marcinkiewicz Multiplier Theorem for T
 8.3. The Strong Marcinkiewicz Multiplier Theorem for ?
 8.4. The Strong Marcinkiewicz Multiplier Theorem for ?
 8.5. Decompositions which are not Hadamard
 9. Applications of the LittlewoodPaley Theorem
 9.1. Some General Results
 9.2. Construction of ?(p) Sets in ?
 9.3. Singular Multipliers
 Appendix A. Special Cases of the Marcinkiewicz Interpolation Theorem
 A.1. The Concepts of Weak Type and Strong Type
 A.2. The Interpolation Theorems
 A.3. VectorValued Functions
 Appendix B. The Homomorphism Theorem for Multipliers...
 B.1. The Key Lemmas
 B.2. The Homomorphism Theorem
 Appendix D. Bernstein’s Inequality
 D.1. Bernstein’s Inequality for ?
 D.2. Bernstein’s Inequality for T
 D.3. Bernstein’s Inequality for LCA Groups
 Dyadic Intervals
 7.1. Introduction
 7.2. The LittlewoodPaley Theorem: First Approach
 7.3. The LittlewoodPaley Theorem: Second Approach
 7.4. The LittlewoodPaley Theorem for Finite Products of ?, Tand ?: Dyadic Intervals