Nonlocal Gagliardo-Nirenberg-Sobolev type inequality
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arXiv
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| Format: | Preprint |
| Published: |
2021
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| _version_ | 1866912160404209664 |
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| author | Foghem, Guy |
| author_facet | Foghem, Guy |
| contents | We establish Gagliardo-Nirenberg-Sobolev type inequalities on nonlocal Sobolev spaces driven by $p$-Lévy integrable kernels, by imposing some appropriate growth conditions on the associated critical function. This naturally allows to devise Sobolev embeddings, as well as, compact embeddings of nonlocal Sobolev spaces into Orlicz type spaces. The Gagliardo-Nirenberg-Sobolev type inequalities, as in the classical context, turn out to have some reciprocity with Poincaré and Poincaré-Sobolev type inequalities. The classical fractional Sobolev inequality is also derived as a direct consequence. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2105_07989 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Nonlocal Gagliardo-Nirenberg-Sobolev type inequality Foghem, Guy Analysis of PDEs 39B62, 46E30, 46E35, 46E39, 47G20 We establish Gagliardo-Nirenberg-Sobolev type inequalities on nonlocal Sobolev spaces driven by $p$-Lévy integrable kernels, by imposing some appropriate growth conditions on the associated critical function. This naturally allows to devise Sobolev embeddings, as well as, compact embeddings of nonlocal Sobolev spaces into Orlicz type spaces. The Gagliardo-Nirenberg-Sobolev type inequalities, as in the classical context, turn out to have some reciprocity with Poincaré and Poincaré-Sobolev type inequalities. The classical fractional Sobolev inequality is also derived as a direct consequence. |
| title | Nonlocal Gagliardo-Nirenberg-Sobolev type inequality |
| topic | Analysis of PDEs 39B62, 46E30, 46E35, 46E39, 47G20 |
| url | https://arxiv.org/abs/2105.07989 |