Hankel operators on the weighted Bergman spaces with exponential type weights

Abstract

Let$AL_\varphi ^2 \left( \mathbb{D} \right)$ denote the closed subspace of$L^2 \left( {\mathbb{D},e^{ - 2\varphi } dA} \right)$ consisting of analytic functions in the unit disk$\mathbb{D}$. For certain class of subharmonic$\varphi :\mathbb{D} \to \mathbb{Z}$, the Hankel operatorH _b on$AL_\varphi ^2 \left( \mathbb{D} \right)$ with symbol$b \in L^2 \left( \mathbb{D} \right)$ is studied. Criteria for boundedness and compactness of such kind of Hankel operators are presented.