Upper and lower bounds for essential norm of weighted composition operators from Bergman spaces with Békollé weights (Q2046584)

Summary: Let \(\sigma\) be a weight function such that \(\sigma/(1 - | z|^2)^\alpha\) is in the class \(B_{p_0}(\alpha)\) of Békollé weights, \(\mu\) a normal weight function, \(\psi\) a holomorphic map on \(\mathbb{D}\), and \(\varphi\) a holomorphic self-map on \(\mathbb{D}\). In this paper, we give upper and lower bounds for essential norm of weighted composition operator \(W_{\psi,\varphi}\) acting from weighted Bergman spaces \(\mathscr{A}^{p}(\sigma)\) to Bloch-type spaces \(\mathscr{B}_{\mu}\).