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 Calder\\ on-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 $\\xi_1+\\cdots+\\xi_m=0$.