Analysis Seminar: "Weighted theory of Toeplitz operators on the Bergman space"

Abstract: We study the weighted compactness and boundedness properties of Toeplitz operators on the Bergman space with respect to Bekolle-Bonami type weights. Let  T_u denote the Toeplitz operator on the (unweighted) Bergman space of the unit ball in C^n with symbol u in  L^infty. We give sufficient conditions on u that imply the compactness of T_u on L^p_sigma for p in [1,\infty) and all weights sigma in the Bekolle-Bonami class B_p . Additionally, using an extrapolation result, we characterize the compact Toeplitz operators on the weighted Bergman space A^p_sigma for all sigma belonging to a nontrivial subclass of B_p. Concerning boundedness, we show that T_u extends boundedly on L^p_sigma for p in (1,\infty) and weights sigma in a u-adapted class of weights containing B_p.  This talk is based on joint work with Cody Stockdale (Clemson University).

Host: John McCarthy