The measures with an associated square function operator bounded in L²

2016/12/14 by Jaye, Benjamin, Nazarov, Fedor, Tolsa, Xavier · 1 citation
#Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA) #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.1612.04754

Abstract

In this paper we provide an extension of a theorem of David and Semmes ('91) to general non-atomic measures. The result provides a geometric characterization of the non-atomic measures for which a certain class of square function operators, or singular integral operators, are bounded in L²(μ). The description is given in terms of a modification of Jones' β-coefficients.

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