Multiplier conditions for Boundedness into Hardy spaces

Abstract

In the present work, we find useful and explicit necessary and sufficient conditions for linear and multilinear multiplier operators of Coifman-Meyer type, finite sum of products of Calderón-Zygmund operators, and also of intermediate types to be bounded from a product of Lebesgue or Hardy spaces into a Hardy space. These conditions state that the symbols of the multipliers $\sigma ({\xi }_1,\dots ,{\xi }_m)$ and their derivatives vanish on the hyperplane ${\xi }_1+\cdots +{\xi }_m=0$.

13 pages