Speaker: Bingyang Hu (Auburn University)

 

Title: From complex models to dyadic methods: A real-variable approach to hypersingular operators 

 

 

Abstract:  This talk consists of two parts. In the first part, we discuss the \(L^p\) theory for hypersingular maximal operators and the hypersingular Bergman projection, with an emphasis on estimates along the critical line where strong-type bounds typically fail. These results offer a systematic extension of the classical Bergman theory, yielding new directions in this area. In the second part, motivated by the phenomena and methods from Part I, we develop a more general framework that applies to a broader class of hypersingular sparse operators. The key new ingredient is the Forelli-Rudin method, which provides a flexible mechanism for establishing weak-type estimates on the critical line.

 

This talk is based on recent joint work with Xiaojing Zhou.

 

 

Host: Le Chen

 

 

 

For more details, please visit https://webhome.auburn.edu/~lzc0090/SASA/20260318_Hu.html.