Fourier Convolution Operators with Symbols Equivalent to Zero at Infinity on Banach Function Spaces

Abstract

We study Fourier convolution operators W0(a) with symbols equivalent to zero at infinity on a separable Banach function space X(ℝ) such that the Hardy-Littlewood maximal operator is bounded on X(ℝ) and on its associate space X′(ℝ). We show that the limit operators of W0(a) are all equal to zero.