Singular integrals of non-convolution type on product spaces

Abstract

We study a new class of pseudo differential operators whose symbols satisfy the differential inequality with a mixture of homogeneities. On the other hand, by taking singular integral realization, it can be equivalently defined by kernels carrying certain characteristic properties on product spaces. We prove that these operators are bounded on L^p-spaces for 1<p<infinity. Moreover, they form an algebra.

arXiv commentWe have corrected a number of errors and typos from the previous version