This is an announcement for the paper "The Littlewood--Paley--Rubio de Francia property of a Banach space for the case of equal intervals" by T. P. Hyt"onen, J. L. Torrea, and D. V. Yakubovich.

Abstract: Let $X$ be a Banach space. It is proved that an analogue of the Rubio de Francia square function estimate for partial sums of the Fourier series of $X$-valued functions holds true for all disjoint collections of subintervals of the set of integers of equal length and for all exponents $p$ greater or equal than 2 if and only if the space $X$ is a UMD space of type 2. The same criterion is obtained for the case of subintervals of the real line and Fourier integrals instead of Fourier series.

Archive classification: math.FA

Mathematics Subject Classification: 42Bxx; 46B20

Remarks: To appear in The Royal Society of Edinburgh Proc. A (Mathematics)

The source file(s), lpr-equal_v6_arx.tex: 41797 bytes, is(are) stored in gzipped form as 0807.2981.gz with size 14kb. The corresponding postcript file has gzipped size 97kb.

Submitted from: dmitry.yakubovich@uam.es

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