[Banach] Abstract of a paper by Tuomas P. Hytonen and Michael T. Lacey

This is an announcement for the paper "Pointwise convergence of vector-valued Fourier series" by Tuomas P. Hytonen and Michael T. Lacey.

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.

Archive classification: math.FA math.CA

Mathematics Subject Classification: 42B20, 42B25

Remarks: 26 pages

Submitted from: tuomas.hytonen@helsinki.fi

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1205.0261

or

http://arXiv.org/abs/1205.0261