Fredholm criteria for Wiener-Hopf operators with continuous symbols acting on some Banach function spaces
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866914042705084416 |
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| author | Valente, Márcio |
| author_facet | Valente, Márcio |
| contents | Let $X(\mathbb{R}_{+})$ be one of the following three Banach function spaces: a Lorentz space $L^{p, q}(\mathbb{R}_{+})$ with $1 < p, q < \infty$; a reflexive Orlicz space $L^Φ(\mathbb{R}_{+})$; or a variable Lebesgue space $L^{p(\cdot)}(\mathbb{R}_{+})$ with variable exponent $p(\cdot)\in \mathcal{B}_{M}(\mathbb{R})$. We extend the Fredholm criteria for Wiener-Hopf operators with continuous symbols on the Lebesgue space $L^{p}(\mathbb{R}_{+})$, $1 < p < \infty$, obtained by Roland Duduchava in the late 1970s, to the space $X(\mathbb{R}_{+})$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_13996 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Fredholm criteria for Wiener-Hopf operators with continuous symbols acting on some Banach function spaces Valente, Márcio Functional Analysis 47B35 (Primary), 46E30 (Secondary) Let $X(\mathbb{R}_{+})$ be one of the following three Banach function spaces: a Lorentz space $L^{p, q}(\mathbb{R}_{+})$ with $1 < p, q < \infty$; a reflexive Orlicz space $L^Φ(\mathbb{R}_{+})$; or a variable Lebesgue space $L^{p(\cdot)}(\mathbb{R}_{+})$ with variable exponent $p(\cdot)\in \mathcal{B}_{M}(\mathbb{R})$. We extend the Fredholm criteria for Wiener-Hopf operators with continuous symbols on the Lebesgue space $L^{p}(\mathbb{R}_{+})$, $1 < p < \infty$, obtained by Roland Duduchava in the late 1970s, to the space $X(\mathbb{R}_{+})$. |
| title | Fredholm criteria for Wiener-Hopf operators with continuous symbols acting on some Banach function spaces |
| topic | Functional Analysis 47B35 (Primary), 46E30 (Secondary) |
| url | https://arxiv.org/abs/2509.13996 |