Abstract of a paper by T. P. Hyt\"onen, J. L. Torrea, and D. V. Yakubovich
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 The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0807.2981 or http://arXiv.org/abs/0807.2981 or by email in unzipped form by transmitting an empty message with subject line uget 0807.2981 or in gzipped form by using subject line get 0807.2981 to: math@arXiv.org.
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