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

Krystian Kazaniecki, Michał Wojciechowski

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 a…