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Bergman projection induced by radial weight
Advances in Mathematics ( IF 1.5 ) Pub Date : 2021-08-17 , DOI: 10.1016/j.aim.2021.107950
José Ángel Peláez 1 , Jouni Rättyä 2
Affiliation  

We establish characterizations of the radial weights ω on the unit disc such that the Bergman projection Pω, induced by ω, is bounded and/or acts surjectively from L to the Bloch space B, or the dual of the weighted Bergman space Aω1 is isomorphic to the Bloch space under the Aω2-pairing. We also solve the problem posed by Dostanić in 2004 of describing the radial weights ω such that Pω is bounded on the Lebesgue space Lωp, under a weak regularity hypothesis on the weight involved. With regard to Littlewood-Paley estimates, we characterize the radial weights ω such that the norm of any function in Aωp is comparable to the norm in Lωp of its derivative times the distance from the boundary. This last-mentioned result solves another well-known problem on the area. All characterizations can be given in terms of doubling conditions on moments and/or tail integrals r1ω(t)dt of ω, and are therefore easy to interpret.



中文翻译:

径向权重引起的伯格曼投影

我们在单位圆盘上建立径向权重ω 的特征,使得伯格曼投影ω,由ω诱导,有界和/或从 到布洛赫空间 ,或加权伯格曼空间的对偶 ω1 与 Bloch 空间同构 ω2-配对。我们还解决了 Dostanić 在 2004 年提出的描述径向权重ω 的问题,使得ω 在 Lebesgue 空间上有界 ω,在所涉及的权重的弱规律性假设下。关于 Littlewood-Paley 估计,我们刻画径向权重ω,使得任何函数的范数在ω 与标准中的标准相当 ω其导数乘以到边界的距离。最后提到的这个结果解决了该地区另一个众所周知的问题。所有特征都可以根据矩和/或尾积分的加倍条件给出r1ω()dω,因此是很容易理解。

更新日期:2021-08-19
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