In this paper, we investigate the Toeplitz operators on the weighted Bergman spaces. It is shown that if S is the finite sum of finite product of Toeplitz operators, then S is compact iff the Berezin transform of S vanishes at the boundary of the unit disk.
Tao YU,Shan Li SUN.
Compact Toeplitz Operators on the Weighted Bergman Spaces. Acta Mathematica Sinica, Chinese Series, 2001, 44(2): 233-240 https://doi.org/10.12386/A2001sxxb0032