HP-VARIANTS AND LP-VARIANTS OF MULTIPARAMETER CALDERON-ZYGMUND THEORY

We consider Calderon-Zygmund operators on product domains. Under certain weak conditions on the kernel a singular integral operator can be proved to be bounded on H(p)(R x R x ... x R) , 0 < p less-than-or-equal-to 1, if its behaviour on L2 and on certain scalar-valued and vector-valued rectangle atoms is known. Another result concerns an extension of the authors' results on L(p)-variants of Calderon-Zygmund theory [1, 23] to the product-domain-setting. As an application, one obtains estimates for Fourier multipliers and pseudo-differential operators.