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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ba60-3-7,
author = {Tuomas P. Hyt\"onen},
title = {Vector-Valued Singular Integrals Revisited-with Random Dyadic Cubes},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
volume = {60},
year = {2012},
pages = {269-283},
zbl = {1254.42026},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba60-3-7}
}
Tuomas P. Hytönen. Vector-Valued Singular Integrals Revisited-with Random Dyadic Cubes. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 60 (2012) pp. 269-283. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba60-3-7/