Foundations of vector-valued singular integrals revisited---with random dyadic cubes
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🧮 math.FA
math.CA
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cubesdyadicrandomvector-valuedallowsanalysisapproacharguments
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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 to circumvent the most subtle parts of the original arguments.
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