Analysis Seminar: "Wavelet representation of singular integral operators"
Abstract: I will report on recent joint work with Brett Wick and Tyler Willams. In this work we set forth a new method of representation for singular integrals of Calderon-Zygmund type in both one and two parameters. Unlike previous dyadic-probabilistic techniques, our representation detects additional smoothness properties of the operator in question. Among the main consequences, motivated by further applications to theory of quasiconformal mappings and PDE, we derive sharp weighted estimates for smooth and non-smooth Calderon-Zygmund operators in one and two parameters on Sobolev spaces.
Host: John McCarthy