Noncommutative Geometry Seminar

Date: March 28, 2018

Time: 2:00PM - 2:50PM

Location: BLOC 628

Speaker: Yi Wang, Texas A&M University

Title: Poincare type inequality and the Arveson-Douglas Conjecture

Abstract: The Poincare inequality says that the Lp norm of a function is controlled by its gradient. Boas and Straube improved that inequality by adding a weight function on the gradient. By applying this inequality on the Hardy and Bergman spaces on bounded strongly pseudoconvex domains with smooth boundary, we show that the Hardy norm of a function is equivalent to a weighted Bergman norm of its gradient. This allows us to apply existing techniques for submodules of the Bergman module, and obtain essential normality for principal submodules of the Hardy module.