Hormander-Mikhlin type theorem on non-commutative spaces
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866908872532295680 |
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| author | Akylzhanov, Rauan Ruzhansky, Michael Tulenov, Kanat |
| author_facet | Akylzhanov, Rauan Ruzhansky, Michael Tulenov, Kanat |
| contents | In this paper, we introduce a Fourier-type formalism on non-commutative spaces. As a result, we obtain two versions of Hormander-Mikhlin Lp-multiplier theorem: on locally compact Kac groups and on semi-finite von Neumann algebras, respectively. In the simplest case our result coincides with a sharp version of the classical Hormander Lp-multiplier theorem, which was obtained by Grafakos and Slavikova in [11]. Finally, we present some applications to the evolution equation in non-commutative setting. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_01240 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Hormander-Mikhlin type theorem on non-commutative spaces Akylzhanov, Rauan Ruzhansky, Michael Tulenov, Kanat Operator Algebras Quantum Algebra In this paper, we introduce a Fourier-type formalism on non-commutative spaces. As a result, we obtain two versions of Hormander-Mikhlin Lp-multiplier theorem: on locally compact Kac groups and on semi-finite von Neumann algebras, respectively. In the simplest case our result coincides with a sharp version of the classical Hormander Lp-multiplier theorem, which was obtained by Grafakos and Slavikova in [11]. Finally, we present some applications to the evolution equation in non-commutative setting. |
| title | Hormander-Mikhlin type theorem on non-commutative spaces |
| topic | Operator Algebras Quantum Algebra |
| url | https://arxiv.org/abs/2503.01240 |