Trace ideal criteria for Toeplitz and Hankel operators on the weighted Bergman spaces with exponential type weights (Q1919924)

Let \(\varphi: \mathbb{D}\to \mathbb{R}\) be a subharmonic function and let \(AL^2_\varphi(\mathbb{D})\) denote the closed subspace of \(L^2(\mathbb{D}, e^{- 2\varphi} dA)\) consisting of analytic functions in the unit disk \(\mathbb{D}\). For a certain class of subharmonic \(\varphi\), the necessary and sufficient conditions are obtained for the Toeplitz operator \(T_\mu\) on \(AL^2_\varphi(\mathbb{D})\) and the Hankel operator \(H_b\) on \(AL^2_\varphi(\mathbb{D})\) in order that they belong to the Schatten-von Neumann class \(S_p\).