Abstract

We study Fourier convolution operators W 0(a) with symbols equivalent to zero at infinity on a separable Banach function space $$X(\mathbb {R})$$ such that the Hardy-Littlewood maximal operator is bounded on $$X(\mathbb {R})$$ and on its associate space $$X'(\mathbb {R})$$ . We show that the limit operators of W 0(a) are all equal to zero.

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