On the continuity of Fourier multipliers on the homogeneous Sobolev spaces $\dot{W}^1_1(R^d)$

Abstract

In this paper we proof that every Fourier multiplier on homogeneous sobolev space $\dot{W}_1^1(\mathbb{R}^d)$ is a continuous function. Our theorem is generalization of A. Bonami and S. Poornima result for Fourier multipliers, which are homogeneous functions of degree zero.