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...
Springer Berlin Heidelberg
|Edition:||1st ed. 1977|
|Series:||Ergebnisse der Mathematik und ihrer Grenzgebiete. 2. Folge, A Series of Modern Surveys in Mathematics
|Collection:||Springer Book Archives -2004 - Collection details see MPG.ReNa|
- 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
- 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
- Dyadic Intervals
- 7.1. Introduction
- 7.2. The Littlewood-Paley Theorem: First Approach
- 7.3. The Littlewood-Paley Theorem: Second Approach
- 7.4. The Littlewood-Paley Theorem for Finite Products of ?, Tand ?: Dyadic Intervals