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arXiv · 2509.17451

Maximal Noncompactness of Wiener-Hopf Operators

Oleksiy Karlovych·Eugene Shargorodsky
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Abstract

Let $X(\mathbb{R})$ be a separable translation-invariant Banach function space and $a$ be a Fourier multiplier on $X(\mathbb{R})$. We prove that the Wiener-Hopf operator $W(a)$ with symbol $a$ is maximally noncompact on the space $X(\mathbb{R}_+)$, that is, its Hausdorff measure of noncompactness, its essential norm and its norm are all equal. This equality for the Hausdorff measure of noncompactness of $W(a)$ is new even in the case of $X(\mathbb{R})=L^p(\mathbb{R})$ with $1\le p<\infty$.

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Oleksiy Karlovych, Eugene Shargorodsky. 2025-09-22. Maximal Noncompactness of Wiener-Hopf Operators. https://arxiv.org/abs/2509.17451

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