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.