A note on continuity of strongly singular Calderón-Zygmund operators in Hardy-Morrey spaces

Abstract

In this note we address the continuity of strongly singular Calderón-Zygmund operators on Hardy-Morrey spaces ${\mathcal{H}\mathcal{M}}_q^{\lambda }({\mathbb{R}}^n)$, assuming weaker integral conditions on the associated kernel. Important examples that falls into this scope are pseudodifferential operators on the Hörmander classes $Op{S}_{\sigma ,\mu }^m({\mathbb{R}}^n)$ with $0<\sigma \le 1$, $0\le \mu <1$, $\mu \le \sigma$ and $m\le -n(1-\sigma )/2$.