Weighted inequalities for sub-monotone functionals
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866910870946185216 |
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| author | Gogatishvili, Amiran Pick, Luboš |
| author_facet | Gogatishvili, Amiran Pick, Luboš |
| contents | We establish a set of relations between several quite diverse types of weighted inequalities involving various integral operators and fairly general quasinorm-like functionals which we call sub-monotone. The main result enables one to solve a specific problem by transferring it to another one for which a solution is known. The main result is formulated in a rather surprising generality, involving previously unknown cases, and it works even for some nonlinear operators such as the geometric or harmonic mean operators. Proofs use only elementary means. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_20115 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Weighted inequalities for sub-monotone functionals Gogatishvili, Amiran Pick, Luboš Classical Analysis and ODEs Analysis of PDEs Functional Analysis 26D15, 46E30, 47G10 We establish a set of relations between several quite diverse types of weighted inequalities involving various integral operators and fairly general quasinorm-like functionals which we call sub-monotone. The main result enables one to solve a specific problem by transferring it to another one for which a solution is known. The main result is formulated in a rather surprising generality, involving previously unknown cases, and it works even for some nonlinear operators such as the geometric or harmonic mean operators. Proofs use only elementary means. |
| title | Weighted inequalities for sub-monotone functionals |
| topic | Classical Analysis and ODEs Analysis of PDEs Functional Analysis 26D15, 46E30, 47G10 |
| url | https://arxiv.org/abs/2407.20115 |