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Littlewood-Paley and Multiplier Theory

This book is intended to be a detailed and carefully written account of various versions of the Littlewood-Paley 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 self-contained and un...

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Bibliographic Details
Main Authors: Edwards, R. E., Gaudry, G. I. (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:
Mathematical Analysis
Analysis
Online Access:
Collection: Springer Book Archives -2004 - Collection details see MPG.ReNa
Table of Contents:
  • Prologue
  • 1. Introduction
  • 1.1. Littlewood-Paley 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 (Scalar-Valued Case)
  • 2.1. Covering Families
  • 2.2. The Covering Lemma
  • 2.3. The Decomposition Theorem
  • 2.4. Bounds for Convolution Operators
  • 3. Convolution Operators (Vector-Valued Case)
  • 3.1. Introduction
  • 3.2. Vector-Valued Functions
  • 3.3. Operator-Valued Kernels
  • 3.4. Fourier Transforms
  • 3.5. Convolution Operators
  • 3.6. Bounds for Convolution Operators
  • 4. The Littlewood-Paley Theorem for Certain Disconnected Groups
  • 4.1. The Littlewood-Paley Theorem for a Class of Totally Disconnected Groups
  • 4.2. The Littlewood-Paley Theorem for a More General Class of Disconnected Groups?
  • 4.3. A Littlewood-Paley 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 Littlewood-Paley 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 Littlewood-Paley 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. Vector-Valued 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
  • 5. Martingales and the Littlewood-Paley Theorem
  • 5.1. Conditional Expectations
  • 5.2. Martingales and Martingale Difference Series
  • 5.3. The Littlewood-Paley Theorem
  • 5.4. Applications to Disconnected Groups
  • 6. The Theorems of M. Riesz and Steckin for ?, Tand ?
  • 6.1. Introduction
  • 6.2. The M. Riesz, Conjugate Function, and Ste?kin Theorems for ?
  • 6.3. The M. Riesz, Conjugate Function, and Ste?kin Theorems for T
  • 6.4. The M. Riesz, Conjugate Function, and Ste?kin Theorems for ?
  • 6.5. The Vector Version of the M. Riesz Theorem for ?, Tand ?
  • 6.6. The M. Riesz Theorem for ?k × Tm × ?n
  • 6.7. The Hilbert Transform
  • 6.8. A Characterisation of the Hilbert Transform
  • 7. The Littlewood-Paley Theorem for ?, Tand ?: Dyadic Intervals
  • 7.1. Introduction
  • 7.2. The Littlewood-Paley Theorem: FirstApproach
  • 7.3. The Littlewood-Paley Theorem: Second Approach
  • 7.4. The Littlewood-Paley Theorem for Finite Products of ?, Tand ?: Dyadic Intervals

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