无限维多圆盘中的Fatou与Riesz兄弟定理
复变函数
2017-10-23 v2 泛函分析
摘要
我们研究无限维多圆盘上Hardy空间中函数的边界行为。这些空间与Dirichlet级数的Hardy空间密切相关。我们展示了关于径向收敛的几个Fatou和Marcinkiewicz-Zygmund型定理。作为推论，人们得到了无限维中F.和M. Riesz兄弟定理的简易新证明。最后，我们提供反例表明，即使对于有界解析函数，在不限制径向收敛模式的情况下，逐点Fatou定理在无限维中也不成立。
引用
@article{arxiv.1512.01509,
title = {Fatou and brother Riesz theorems in the infinite-dimensional polydisc},
author = {Alexandru Aleman and Jan-Fredrik Olsen and Eero Saksman},
journal= {arXiv preprint arXiv:1512.01509},
year = {2017}
}
备注
17 pages. In this version, Theorem 1 has been corrected. As a consequence, Theorem 2 and Corollary 4 have been modified, and Corollary 5 (in the enumeration of the previous version) has been removed