Results on Weighted Norm Inequalities for Multipliers

Weighted -norm inequalities are derived for multiplier operators on Euclidean space. The multipliers are assumed to satisfy conditions of the Hörmander-Mikhlin type, and the weight functions are generally required to satisfy conditions more restrictive than which depend on the degree of differentiability of the multiplier. For weights which are powers of <!-- MATH $\left| x \right|$ --> , sharp results are obtained which indicate such restrictions are necessary. The method of proof is based on the function of C. Fefferman and E. Stein rather than on Littlewood-Paley theory. The method also yields results for singular integral operators.