Optimal function spaces in weighted Sobolev embeddings with $α$-homogeneous weights
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866918087761068032 |
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| author | Drážný, Ladislav |
| author_facet | Drážný, Ladislav |
| contents | We study weighted Sobolev inequalities on open convex cones endowed with $α$-homogeneous weights satisfying a certain concavity condition. We establish a so-called reduction principle for these inequalities and characterize optimal rearrangement-invariant function spaces for these weighted Sobolev inequalities. Both optimal target and optimal domain spaces are characterized. Abstract results are accompanied by general yet concrete examples of optimal function spaces. For these examples, the class of so-called Lorentz--Karamata spaces, which contains in particular Lebesgue spaces, Lorentz spaces, and some Orlicz spaces, is used. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_07806 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Optimal function spaces in weighted Sobolev embeddings with $α$-homogeneous weights Drážný, Ladislav Functional Analysis 46E30, 46E35 We study weighted Sobolev inequalities on open convex cones endowed with $α$-homogeneous weights satisfying a certain concavity condition. We establish a so-called reduction principle for these inequalities and characterize optimal rearrangement-invariant function spaces for these weighted Sobolev inequalities. Both optimal target and optimal domain spaces are characterized. Abstract results are accompanied by general yet concrete examples of optimal function spaces. For these examples, the class of so-called Lorentz--Karamata spaces, which contains in particular Lebesgue spaces, Lorentz spaces, and some Orlicz spaces, is used. |
| title | Optimal function spaces in weighted Sobolev embeddings with $α$-homogeneous weights |
| topic | Functional Analysis 46E30, 46E35 |
| url | https://arxiv.org/abs/2407.07806 |