Hankel forms and measures on weighted Bergman spaces

2024/09/26 by Eskandari, Setareh, Perälä, Antti
#Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.2409.17709

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^p_ω Hankel measures for p≤ 2. The proofs leverage the existing theory of weighted Bergman spaces and the recent results on two-weight fractional derivatives, also simplifying the recent A¹ duality for small Bergman spaces obtained by Peláez and Rättyä.

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