Time-frequency representations on Lorentz spaces over locally compact Abelian groups
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866908562756730880 |
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| author | Liu, Jun Lu, Yaqian Yan, Xianjie Zhang, Chi |
| author_facet | Liu, Jun Lu, Yaqian Yan, Xianjie Zhang, Chi |
| contents | Let $G$ be a locally compact Abelian group with a fixed Haar measure and, denote by $\widehat{G}$ its dual group. In this article, the authors obtain various boundedness of the short-time Fourier transform on Lorentz spaces: $$L^{p_1,u}(G)\times L^{p_2,v}(G)\to L^{q,w}(G\times\widehat{G})$$ with the indexes satisfying appropriate relations. These results are then used to prove the corresponding boundedness of $τ$-Wigner transforms and $τ$-Weyl operators. As an application, the Lieb's uncertainty principle in the context of Lorentz spaces is finally investigated. All these results are new even for the case when $G$ is finite. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_23296 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Time-frequency representations on Lorentz spaces over locally compact Abelian groups Liu, Jun Lu, Yaqian Yan, Xianjie Zhang, Chi Classical Analysis and ODEs Functional Analysis Let $G$ be a locally compact Abelian group with a fixed Haar measure and, denote by $\widehat{G}$ its dual group. In this article, the authors obtain various boundedness of the short-time Fourier transform on Lorentz spaces: $$L^{p_1,u}(G)\times L^{p_2,v}(G)\to L^{q,w}(G\times\widehat{G})$$ with the indexes satisfying appropriate relations. These results are then used to prove the corresponding boundedness of $τ$-Wigner transforms and $τ$-Weyl operators. As an application, the Lieb's uncertainty principle in the context of Lorentz spaces is finally investigated. All these results are new even for the case when $G$ is finite. |
| title | Time-frequency representations on Lorentz spaces over locally compact Abelian groups |
| topic | Classical Analysis and ODEs Functional Analysis |
| url | https://arxiv.org/abs/2509.23296 |