On Hardy spaces on worm domains

IF 0.3 Q4 MATHEMATICS
A. Monguzzi
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引用次数: 8

Abstract

Abstract In this review article we present the problem of studying Hardy spaces and the related Szeg˝o projection on worm domains. We review the importance of the Diederich–Fornæss worm domain as a smooth bounded pseudoconvex domain whose Bergman projection does not preserve Sobolev spaces of sufficiently high order and we highlight which difficulties arise in studying the same problem for the Szeg˝o projection. Finally, we announce and discuss the results we have obtained so far in the setting of non-smooth worm domains.
关于蠕虫域上的Hardy空间
摘要本文主要讨论了Hardy空间的研究问题以及相关的蠕虫域上的Szeg“o投影问题。我们回顾了Diederich-Fornæss蠕虫域作为光滑有界伪凸域的重要性,其Bergman投影不能保留足够高阶的Sobolev空间,并强调了在研究相同问题时出现的困难。最后,我们公布并讨论了目前为止在非光滑蠕虫域设置下得到的结果。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Concrete Operators
Concrete Operators MATHEMATICS-
CiteScore
1.00
自引率
16.70%
发文量
10
审稿时长
22 weeks
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