Hankel forms and measures on weighted Bergman spaces

Abstract

We characterize the boundedness of Hankel forms and Hankel operators induced by measures on weighted Bergman spaces, where the weights satisfy an upper-doubling condition. We also characterize $A_{\omega }^p$ Hankel measures for $p\le 2$. The proofs leverage the existing theory of weighted Bergman spaces and the recent results on two-weight fractional derivatives, also simplifying the recent $A^1$ duality for small Bergman spaces obtained by Peláez and Rättyä.

12 pages