Weighted norm inequalities for derivatives on Bergman spaces
An equivalent norm in the weighted Bergman space $A^p_ω$, induced by an $ω$ 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 $A^p_ω$ and the boundedness of a Hörmander-type maximal function. Results obtained are further applied to describe the resolvent set of the integral operators $T_g(f)(z)=\int_0^z g'(ζ)f(ζ)\,dζ$ acting on $A^p_ω$.
math.CV↗