English

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 T(1)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.

Keywords

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}
}

Comments

12 pages

R2 v1 2026-06-21T19:26:11.899Z