Table of Contents
§0. Introduction 1
I. The interpolation of "local" spaces
§1. Notations and definitions 12
§2. Stability under complex interpolation 17
§3. Interpolation of multiplier theorems 23
II. Families of Banach spaces
§4. Taibelson spaces and spaces of Bessel potentials 26
§5. The properties of localizations of spaces of
Lipschitz type 32
§6. Spaces of sequences 46
III. The theory of ultraspherical multipliers
§7. The ultraspherical convolution 57
§8. A Littlewood-Paley Theory for ultraspherical series 60
§9- A full range multiplier Theorem for q = 2 66
§10. The interpolation of ultraspherical multiplier
theorems 75
§11. Some of these results are best possible 79
IV. Applications to other expansions
§12. Multiplier theorems for Hankel transforms and
spaces of radial functions 82
§13. Multipliers for spherical harmonic expansions 84
§l4. Multipliers for Jacob! expansions 85
Figures 87
Table of notation 90
Bibliography 91
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