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.

arXiv comment16 pages

Cited by in corpus (1)

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