• Bingyang Hu
• Assistant Professor
• Auburn University
• Date: March 18, Wednesday, 2026
• Time: 14:00-14:50
• Host: Le Chen
• Room: Parker 328
• 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.

Note: This talk also serves as Bingyang Hu's third-year review.