Prefer a chat interface with context about you and your work?
On the continuity of Fourier multipliers on the homogeneous Sobolev spaces ${\dot{W}^1_1(R^d)}$
In this paper we prove that every Fourier multiplier on the homogeneous Sobolev space W ˙ 1 1 (ℝ d ) is a continuous function. This theorem is a generalization of the result of A. Bonami and S. Poornima for Fourier multipliers, which are homogeneous functions of degree zero.