Alper Balci
The Ohio State University
Title
Harmonic Bergman Kernel and Projection on Annular Regions
Abstract
Harmonic Bergman spaces are much less studied compared to their holomorphic counterparts. Harmonic Bergman kernel is known only in a handful of cases, such as when the domain is the unit ball, upper half space or exterior of the ball. In this talk, we obtain a previously unknown series representation for the harmonic Bergman kernel on annular regions and we prove a related decomposition theorem. Moreover, we provide a complete characterization of the values of $p$ for which the corresponding harmonic Bergman projection is bounded on $L^p$, including the cases in which the inner radius is zero or the outer radius is $\infty$. We observe some interesting sharp dimension-dependent behavior.