The Littlewood—Paley—Rubio de Francia property of a Banach space for the case of equal intervals
Published online by Cambridge University Press: 08 July 2009
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 ≥ 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.
- Type
- Research Article
- Information
- Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 139 , Issue 4 , August 2009 , pp. 819 - 832
- Copyright
- Copyright © Royal Society of Edinburgh 2009
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