This is an announcement for the paper "Foundations of vector-valued singular integrals revisited---with random dyadic cubes" by Tuomas P. Hytonen.

Abstract: 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.

Archive classification: math.FA math.CA

Mathematics Subject Classification: 42B20, 60G46

Remarks: 12 pages

Submitted from: tuomas.hytonen@helsinki.fi

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1110.5826

or

http://arXiv.org/abs/1110.5826