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arXiv · 2607.10742

Strong and weak-type estimates for radial weighted Bergman projections

Yuerang Li·Zipeng Wang
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Abstract

We completely characterize the $L^p$-boundedness and the weak-type (1,1) estimate of radial weighted Bergman projections on the unit disk. Our result, in particular, confirms a conjecture proposed by Pel\'{a}ez and R\"{a}tty\"{a} in 2021 and thereby settles a longstanding problem in the area that was formally posed by Dostani\'{c} in 2004. Consequently, we establish the dichotomy that a radial weighted Bergman projection is bounded either only for $p=2$, or for all $p\in(1,\infty)$.

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Yuerang Li, Zipeng Wang. 2026-07-12. Strong and weak-type estimates for radial weighted Bergman projections. https://arxiv.org/abs/2607.10742

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