Vector-Valued Singular Integrals Revisited—with Random Dyadic Cubes
Volume 60 / 2012
Bulletin Polish Acad. Sci. Math. 60 (2012), 269-283
MSC: 42B20, 60G46.
DOI: 10.4064/ba60-3-7
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 one to circumvent the most subtle parts of the original arguments.
