Pointwise convergence of vector-valued Fourier series
Functional Analysis
2015-09-02 v1 Classical Analysis and ODEs
Abstract
We prove a vector-valued version of Carleson's theorem: Let Y=[X,H]_t be a complex interpolation space between a UMD space X and a Hilbert space H. For p\in(1,\infty) and f\in L^p(T;Y), the partial sums of the Fourier series of f converge to f pointwise almost everywhere. Apparently, all known examples of UMD spaces are of this intermediate form Y=[X,H]_t. In particular, we answer affirmatively a question of Rubio de Francia on the pointwise convergence of Fourier series of Schatten class valued functions.
Keywords
Cite
@article{arxiv.1205.0261,
title = {Pointwise convergence of vector-valued Fourier series},
author = {Tuomas P. Hytönen and Michael T. Lacey},
journal= {arXiv preprint arXiv:1205.0261},
year = {2015}
}
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26 pages