A class of linear operators on Bergman spaces

Abstract

We study the boundedness of the linear operator $S$ on $L_a^p(d{A}_{\hat{I}}\pm )$ $(0<p<\infty )$. In particular, we obtain a sufficient and necessary condition for the compactness of the linear operator $S$ on $L_a^p(d{A}_{\hat{I}}\pm )$ $(1<p<\infty )$. Our results weaken the assumptions of earlier results of J. Miao and D. Zheng in a certain sense.

17 pages