Weighted norm inequalities for derivatives on Bergman spaces

Abstract

An equivalent norm in the weighted Bergman space $A_{\omega }^p$, induced by an $\omega$ in a certain large class of non-radial weights, is established in terms of higher order derivatives. Other Littlewood-Paley inequalities are also considered. On the way to the proofs, we characterize the $q$-Carleson measures for the weighted Bergman space $A_{\omega }^p$ and the boundedness of a Hörmander-type maximal function. Results obtained are further applied to describe the resolvent set of the integral operators $T_g(f)(z)={\int }_0^z{g}^{\prime }(\zeta )f(\zeta )d\zeta$ acting on $A_{\omega }^p$.

References in corpus (1)

• Embedding theorems for Bergman spaces via harmonic analysis

Cited by in corpus (1)

• Littlewood-Paley inequalities for fractional derivative on Bergman spaces