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arXiv · 1909.13538

Fourier convolution operators with symbols equivalent to zero at infinity on Banach function spaces

Cláudio A. Fernandes·Alexei Yu. Karlovich·Yuri I. Karlovich
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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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Cláudio A. Fernandes, Alexei Yu. Karlovich, Yuri I. Karlovich. 2019-09-30. Fourier convolution operators with symbols equivalent to zero at infinity on Banach function spaces. https://arxiv.org/abs/1909.13538

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