On the continuity of strongly singular Calderón-Zygmund-type operators on Hardy spaces

Abstract

In this work, we establish results on the continuity of strongly singular Calderón-Zygmund operators of type $\sigma$ on Hardy spaces $H^p({\mathbb{R}}^n)$ for $0<p\le 1$ assuming a weaker $L^s-$type Hörmander condition on the kernel. Operators of this type include appropriated classes of pseudodifferential operators $Op{S}_{\sigma ,b}^m({\mathbb{R}}^n)$ and operators associated to standard $\delta$-kernels of type $\sigma$ introduced by Álvarez and Milman. As application, we show that strongly singular Calderón-Zygmund operators are bounded from $H_w^p({\mathbb{R}}^n)$ to $L_w^p({\mathbb{R}}^n)$, where $w$ belongs to a special class of Muckenhoupt weight.

30 pages