Foundations of vector-valued singular integrals revisited---with random dyadic cubes
Functional Analysis
2011-10-27 v1 Classical Analysis and ODEs
Abstract
The vector-valued theorem due to Figiel, and a certain square function estimate of Bourgain for translations of functions with a limited frequency spectrum, are two cornerstones of harmonic analysis in UMD spaces. In this paper, a simplified approach to these results is presented, exploiting Nazarov, Treil and Volberg's method of random dyadic cubes, which allows to circumvent the most subtle parts of the original arguments.
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Cite
@article{arxiv.1110.5826,
title = {Foundations of vector-valued singular integrals revisited---with random dyadic cubes},
author = {Tuomas P. Hytönen},
journal= {arXiv preprint arXiv:1110.5826},
year = {2011}
}
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12 pages