【摘要】
The theory of Hardy spaces over $\mathbb R^n$, originated by C. Fefferman and Stein, was generalized several decades ago to the case of subsets of $\mathbb R^n$. The pioneering work of generalization was done by Jonsson, Sj\"ogren, and Wallin for the case of suitable closed subsets and by Miyachi for the case of proper open subsets.
In this talk we study Hardy spaces on proper open $\Omega\subset \Bbb R^n$, where $\Omega$ satisfies a doubling condition and $|\Omega|=\infty$.
We first establish a variant of the Calder\'on-Zygmund decomposition, and then explore the relationship among Hardy spaces by means of atomic decomposition, radial maximal function, and grand maximal function.
【报告人简介】
台湾中央大学数学系特聘教授，美国乔治亚大学 1991 年博士。曾任中央大学数学系系主任、理学院副经理等。主要研究兴趣是调和分析，已发表八十余篇数学论文，分别刊登于 Adv. Math., Math. Ann., Trans. AMS, J. Funct. Anal., J. London Math. Soc. 等期刊。
