Generalized Calderón-Zygmund operators on the Hardy space $H_{\rho }^1(\mathcal{X})$

Abstract

Let $(\mathcal{X},d,\mu )$ be an RD-space, and let $\rho$ be an admissible function on $\mathcal{X}$. We establish necessary and sufficient conditions for the boundedness of a new class of generalized Calderón-Zygmund operators of log-Dini type on the Hardy space $H_{\rho }^1(\mathcal{X})$, introduced by Yang and Zhou. Our results extend and unify some recent results, providing further insights into the study of singular integral operators in this setting.

28 pages, Banach J. Math. Anal. (to appear)