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# Analysis Seminar – Walton Green (Washington University)

## October 15, 2021 @ 3:00 pm - 4:00 pm

Title: Wavelet Representation of Smooth Calderón-Zygmund Operators

Abstract: We represent a bilinear Calderón-Zygmund operator at a given smoothness level as a finite sum of cancellative, complexity zero operators, involving smooth wavelet forms, and continuous paraproduct forms. This representation results in a sparse T(1)-type bound, which in turn yields directly new sharp weighted linear and mutlilinear estimates on Lebesgue and Sobolev spaces. Moreover, we apply the representation theorem to study fractional differentiation of bilinear operators, establishing Leibniz-type rules in weighted Sobolev spaces which are new even in the simplest case of the pointwise product.