PhD Thesis Defense: "A Continuous Wavelet Representation for Single and Bi-Parameter Calderón-Zygmund Operators"

Abstract: This thesis develops a novel approach to the representation of singular integral operators of Calderon-Zygmund type in terms of continuous model operators, in both the classical and the bi-parametric setting. These model operators are averages over classes of smooth wavelets and themselves are Calderon-Zygmund operators. A consequence of these representation formulas is a new family of T(1) theorems on weighted Sobolev spaces whose smoothness index is naturally related to kernel smoothness.

Host: Brett Wick