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 σ on Hardy spaces H p (R n ) for 0 < p ≤ 1 assuming a weaker L s −type Hörmander condition on the kernel. Operators of this type include appropriated classes of pseudodifferential operators OpS m σ ,b (R n ) and operators associated to standard δ -kernels of type σ introduced by Álvarez and Milman. As application, we show that strongly singular Calderón-Zygmund operators are bounded from H p w (R n ) to L p w (R n ), where w belongs to a special class of Muckenhoupt weight.