Vector-valued Hausdorff-Young inequality and applications

Abstract

Contents §1. Introduction §2. General definitions and auxiliary results §3. Interpolation spaces §4. Interpolation and the Fourier type of Banach spaces §5. The Rademacher type and cotype §6. The Fourier type of Banach spaces with respect to groups §7. Types and cotypes of Banach spaces with respect to general orthonormal systems §8. Relations between types (cotypes) with respect to the Rademacher system and other orthonormal systems §9. Theorems of Hardy and Paley for vector-valued functions §10. Estimates for Fourier transforms of smooth functions Bibliography