Compact Toeplitz Operators on Pluriharmonic Bergman spaces

OSMAN ABDALLAH ADAM OSMAN

Abstract: On the setting of the unit ball, we characterize compact Toeplitz operators on pluriharmonic Bergman spaces, in terms of the boundary vanishing conditions of the Berezin transform and certain differential quantity of the symbol. As a consequence, we characterize -harmonic and radial symbols of compact Toeplitz operators.

Keywords: Toeplitz Operators, Berezin transform, pluriharmonic function, Bergman spaces