Clemson Analysis and PDE Seminar

Abstract: I will discuss some bad behavior that two-weight norm inequalities for Calderón-Zygmund operators on Lp exhibit that are not present in the well-known (Muckenhoupt) one-weight theory for Singular Integrals. Namely, we will see via some counterexamples that two-weight norms lack a characterization in terms of the weights alone, are unstable under biLipschitz change of variables, and when p not 2, are only known to be characterized by some technical vector-valued conditions. 

Abstract: Classical Clark measures are singular measures on the unit circle defined via inner functions on the disk that are closely tied to important topics in operator theory and complex analysis. In this talk, we’ll review the classical situation, present an analogous definition for two-variable Clark measures on the bidisk, and prove some related results. Specifically, in the rational case, we’ll give exact formulas for these Clark measures, characterize when associated embeddings are unitary, and obtain natural perturbations of pairs of compressed shift operators to pairs of commuting unitary operators. (Time permitting, we'll discuss which results generalize to the non-rational case). This is joint work with John Anderson, Palak Aurora, Linus Bergqvist, Joseph Cima, Conni Liaw, and Alan Sola.

Abstract: TBA

Abstract: TBA