Weighted Bounded Variation Revisited
Fuente:
arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866913133140901888 |
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| author | Bortz, Simon Gossett, Matthew Kasel, Joseph Moen, Kabe |
| author_facet | Bortz, Simon Gossett, Matthew Kasel, Joseph Moen, Kabe |
| contents | In this article, we investigate the theory of weighted functions of bounded variation (BV), as introduced by Baldi [Ba01]. Depending on the theorem, we impose lower semicontinuity and/or a pointwise A1 condition on the weight. Our motivation is twofold: to establish weighted Gagliardo-Nirenberg-Sobolev (GNS) inequalities for BV functions, and to clarify and extend earlier results on weighted BV spaces. Our main contributions include a structure theorem under minimal assumptions (lower semicontinuity), a smooth approximation result, an embedding theorem, a weighted GNS inequality for BV functions, and a corresponding weighted isoperimetric inequality. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_14105 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Weighted Bounded Variation Revisited Bortz, Simon Gossett, Matthew Kasel, Joseph Moen, Kabe Classical Analysis and ODEs Functional Analysis In this article, we investigate the theory of weighted functions of bounded variation (BV), as introduced by Baldi [Ba01]. Depending on the theorem, we impose lower semicontinuity and/or a pointwise A1 condition on the weight. Our motivation is twofold: to establish weighted Gagliardo-Nirenberg-Sobolev (GNS) inequalities for BV functions, and to clarify and extend earlier results on weighted BV spaces. Our main contributions include a structure theorem under minimal assumptions (lower semicontinuity), a smooth approximation result, an embedding theorem, a weighted GNS inequality for BV functions, and a corresponding weighted isoperimetric inequality. |
| title | Weighted Bounded Variation Revisited |
| topic | Classical Analysis and ODEs Functional Analysis |
| url | https://arxiv.org/abs/2510.14105 |