Bochner–Riesz Means on Hardy Spaces Associated with Ball Quasi-Banach Function Spaces

Let X be a ball quasi-Banach function space on Rn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {R}^{n}$$\end{document}. In this article, we obtain the boundedness of the Bochner–Riesz means B1/εδ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$B_{1/\varepsilon }^{\delta }$$\end{document} and the maximal Bochner–Riesz means B∗δ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$B_{*}^{\delta }$$\end{document} on Hardy spaces associated with X. Furthermore, by weakening the assumption that X has an absolutely continuous quasi-norm, the main results in this article can be applied to many concrete spaces such as Morrey spaces. This shows that the results obtained in this article have a wide range of generality.