Strong and weak-type estimates for radial weighted Bergman projections

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 Peláez and Rättyä in 2021 and thereby settles a longstanding problem in the area that was formally posed by Dostanić in 2004. Consequently, we establish the dichotomy that a radial weighted Bergman projection is bounded either only for $p=2$, or for all $p\in (1,\infty )$.

arXiv comment(1)We add the result on the weak-type (1,1) estimate as well as the characterization of the strong and weak-type boundedness of the maximal weighted Bergman projection. (2) The title and the abstract are then changed. (3) All comments are welcome