关于蠕虫域上的Hardy空间

IF 0.3 Q4 MATHEMATICS Concrete Operators Pub Date : 2016-01-13 DOI:10.1515/conop-2016-0005

A. Monguzzi

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引用次数: 8

摘要

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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On Hardy spaces on worm domains

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.

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