Complex symmetric Toeplitz operators on the weighted Bergman space

In this paper, we give a characterization of a complex symmetric Toeplitz operator T-phi on the weighted Bergman space A(alpha)(2)(D). We first give properties of complex symmetric Toeplitz operators T-phi on A(alpha)(2)(D). Next, weprove that if T-phi is complex symmetric with finite symbol, then T-phi is hyponormal on A(alpha)(2)(D) if and only if it is hyponormal on the Hardy space H-2(T). Finally, we consider the complex symmetric Toeplitz operator T-phi on A(alpha)(2)(D) when the conjugation is a special case.