Boundedness of area operators on Bergman spaces

Abstract

We completely characterize the boundedness of the area operators from the Bergman spaces $A_{\alpha }^p({\mathbb{B}}_n)$ to the Lebesgue spaces $L^q({\mathbb{S}}_n)$ for all $0<p,q<\infty$. For the case $n=1$, some partial results were previously obtained by Wu. Especially, in the case $q<p$ and $q<s$, we obtain the new characterizations for the area operators to be bounded. We solve the cases left open there and extend the results to $n$-complex dimension.

arXiv admin note: text overlap with arXiv:1904.00359