Compact embeddings of variable exponent Sobolev, Besov, and Triebel-Lizorkin spaces on metric measure spaces
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866918407483424768 |
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| author | Dymek, Michał |
| author_facet | Dymek, Michał |
| contents | We study compact embeddings of Sobolev, Besov, and Triebel-Lizorkin spaces with variable exponents on both bounded and unbounded metric measure spaces. We establish sufficient conditions for compactness, and under additional assumptions, we show that they are also necessary. Moreover, we investigate the influence of isometry group actions on the compactness of embeddings. In particular, we answer the open question posed by P. Górka in [P. Górka, Looking For Compactness In Sobolev Spaces On Noncompact etric Spaces, Ann. Acad. Sci. Fenn., Vol 43, 2018, 531-540], proving a Berestycki-Lions type theorem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_23671 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Compact embeddings of variable exponent Sobolev, Besov, and Triebel-Lizorkin spaces on metric measure spaces Dymek, Michał Functional Analysis 46E35, 30L99, 42B35 We study compact embeddings of Sobolev, Besov, and Triebel-Lizorkin spaces with variable exponents on both bounded and unbounded metric measure spaces. We establish sufficient conditions for compactness, and under additional assumptions, we show that they are also necessary. Moreover, we investigate the influence of isometry group actions on the compactness of embeddings. In particular, we answer the open question posed by P. Górka in [P. Górka, Looking For Compactness In Sobolev Spaces On Noncompact etric Spaces, Ann. Acad. Sci. Fenn., Vol 43, 2018, 531-540], proving a Berestycki-Lions type theorem. |
| title | Compact embeddings of variable exponent Sobolev, Besov, and Triebel-Lizorkin spaces on metric measure spaces |
| topic | Functional Analysis 46E35, 30L99, 42B35 |
| url | https://arxiv.org/abs/2603.23671 |