RADIAL TOEPLITZ FORMS ON THE WEIGHTED BERGMAN SPACE OVER THE UNIT DISK

Abstract In this paper, the radial Toeplitz forms on the weighted Bergman space over the unit disk are introduced and an analogous result to the Herglotz-Bocher theorem is shown. In other words, an integral representation of the radial Toeplitz sesquilinear forms is given. This approach is then used to show a spectral decomposition of the radial Toeplitz operators with respect to a sesquilinear form. In addition, for each bounded radial operator, we provide an explicit formula for its corresponding covariant symbol and we prove how such an operator can be expressed as an integral operator. Finally, we establish a criterion for a radial Toeplitz form with integral representation using Carleson-type measures.