On Singular Operators in Vanishing Generalized Variable-Exponent Morrey Spaces and Applications to Bergman-Type Spaces

被引：0
作者：
A. N. Karapetyants
H. Rafeiro
S. G. Samko
机构：
[1] Southern Federal University,Department of Mathematical Sciences, College of Sciences
[2] State University of New York,undefined
[3] United Arab Emirates University,undefined
[4] University of Algarve,undefined
来源：
Mathematical Notes | 2019年 / 106卷
关键词：
singular operator; Morrey space; Bergman-type space; Calderon-Zygmund operator;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
We give a proof of the boundedness of the Bergman projection in generalized variable-exponent vanishing Morrey spaces over the unit disc and the upper half-plane. To this end, we prove the boundedness of the Calderón—Zygmund operators on generalized variable-exponent vanishing Morrey spaces. We give the proof of the latter in the general context of real functions on Rn, since it is new in such a setting and is of independent interest. We also study the approximation by mollified dilations and estimate the growth of functions near the boundary.
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页码：727 / 739
页数：12
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