Speaker：Ziyi He（Beijing University of Posts and Telecommunications）

Time：2022-05-19, 16:00

Location：Tencent Meeting ID： 301497640（No Password）

Abstract:

In this talk, we introduce the concept of ball quasi-Banach function spaces $Y(\cx)$ on a space $(\cx,\rho,\mu)$ of homogeneous type. Moreover, we introduce the Hardy space $H_Y(\cx)$ associated with $Y(\cx)$ with some additional assumptions. We also establish the real-variable theory of $H_Y(\cx)$, including various maximal function characterizations, atomic and molecular characterizations, various Littlewood--Paley function characterizations. and the finite atomic characterization. As applications, we obtain the boundedness of Calder\'on--Zygmund operator from $H_Y(\cx)$ to $Y(\cx)$, or to $H_Y(\cx)$. The novelty of this work is that these results have a wide range of generality, and that all these results get rid of the reverse doubling condition of $\mu$ and the triangle inequality of $\rho$.