Foundations of vector-valued singular integrals revisited---with random dyadic cubes

Details Foundations of vector-valued singular integrals revisited---with random dyadic cubes Foundations of vector-valued singular integrals revisited---with random dyadic cubes

2011-10-26

arxiv.org/abs/1110.5826v1

Mathematics

Functional Analysis

12 pages

Scientific paper

The vector-valued $T(1)$ 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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