On the Continuity of Strongly Singular Calderon-Zygmund-Type Operators on Hardy Spaces

In this work, we establish results on the continuity of strongly singular Calderon-Zygmund operators of type s on Hardy spaces H-p(R-n) for 0 < p = 1 assuming a weaker L-s-type Hormander condition on the kernel. Operators of this type include appropriate classes of pseudodifferential operators OpS(s,b)(m)(R-n) and operators associated to standard d- kernels of type s introduced by Alvarez and Milman. As application, we show that strongly singular Calderon-Zygmund operators are bounded from H-w(p)(R-n) to L-w(p)(R-n), where w belongs to a special class of Muckenhoupt weight.