Complex symmetric Toeplitz operators on the Hardy spaces and Bergman spaces.

In this paper, we first completely characterize the complex symmetric Toeplitz operators T φ on the Hardy spaces H 2 (D) with conjugations C p i , j and C n . Next, we give a method to determine the coefficients of φ (z) when T φ is complex symmetric on H 2 (D) with the conjugation C σ , which partially solves a problem raised by [2]. Finally, we consider the complex symmetric Toeplitz operators T φ on the weighted Bergman spaces A 2 (B n) and the pluriharmonic Bergman spaces b 2 (B n) with conjugations C V , where V is a symmetric permutation matrix. [ABSTRACT FROM AUTHOR]