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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


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.


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

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