Author | Edwards, R. E. author |
---|---|
Title | Littlewood-Paley and Multiplier Theory [electronic resource] / by R. E. Edwards, G. I. Gaudry |
Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg, 1977 |
Connect to | http://dx.doi.org/10.1007/978-3-642-66366-6 |
Descript | X, 214 p. online resource |
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 -- 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 ร Tm ร ?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: First Approach -- 7.3. The Littlewood-Paley Theorem: Second Approach -- 7.4. The Littlewood-Paley Theorem for Finite Products of ?, Tand ?: Dyadic Intervals -- 7.5. Fournierโs 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. Bernsteinโs Inequality -- D.1. Bernsteinโs Inequality for ? -- D.2. Bernsteinโs Inequality for T -- D.3. Bernsteinโs Inequality for LCA Groups -- Historical Notes -- References -- Terminology -- Index of Notation -- Index of Authors and Subjects