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Vector-Valued Singular Integrals Revisited—with Random Dyadic Cubes

Volume 60 / 2012

Tuomas P. Hytönen 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.

Authors

  • Tuomas P. HytönenDepartment of Mathematics and Statistics
    University of Helsinki
    Gustaf Hällströmin katu 2b
    FI-00014 Helsinki, Finland
    e-mail

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