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arXiv · 2409.17709

Hankel forms and measures on weighted Bergman spaces

Setareh Eskandari·Antti Perälä
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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 $A^p_\omega$ Hankel measures for $p\leq 2$. 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 Pel\'aez and R\"atty\"a.

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Setareh Eskandari, Antti Perälä. 2024-09-26. Hankel forms and measures on weighted Bergman spaces. https://arxiv.org/abs/2409.17709

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