AI 中文总结
研究单位圆盘上由径向权重诱导的伯格曼投影的\(L^p\)有界性，通过建立二分法及相关条件刻画，证实佩莱兹 - 拉蒂亚猜想，解决多斯塔尼奇在2004年提出的问题。
AI 中文摘要
我们刻画了单位圆盘上由径向权重诱导的伯格曼投影的\(L^p\)有界性，建立了如下二分法：投影要么仅在\(p = 2\)时有界，要么对所有\(p\in(1,\infty)\)都有界。此外，后一种情况成立当且仅当权重满足单边加倍条件。这证实了佩莱兹和拉蒂亚在2021年提出的猜想，从而解决了多斯塔尼奇在2004年正式提出的一个问题。
英文摘要
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 $p\in(1,\infty)$.
Comments(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
