Schur property for jump parts of gradient measures
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866914851094265856 |
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| author | Kazaniecki, Krystian Tselishchev, Anton Wojciechowski, Michał |
| author_facet | Kazaniecki, Krystian Tselishchev, Anton Wojciechowski, Michał |
| contents | We consider weakly null sequences in the Banach space of functions of bounded variation $\mathrm{BV}(\mathbb{R}^d)$. We prove that for any such sequence $\{f_n\}$ the jump parts of the gradients of functions $f_n$ tend to $0$ strongly as measures. It implies that Dunford--Pettis property for the space $\mathrm{SBV}$ is equivalent to the Dunford--Pettis property for the Sobolev space $W^{1,1}.$ |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_08396 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Schur property for jump parts of gradient measures Kazaniecki, Krystian Tselishchev, Anton Wojciechowski, Michał Functional Analysis Classical Analysis and ODEs 26B30, 46E35 We consider weakly null sequences in the Banach space of functions of bounded variation $\mathrm{BV}(\mathbb{R}^d)$. We prove that for any such sequence $\{f_n\}$ the jump parts of the gradients of functions $f_n$ tend to $0$ strongly as measures. It implies that Dunford--Pettis property for the space $\mathrm{SBV}$ is equivalent to the Dunford--Pettis property for the Sobolev space $W^{1,1}.$ |
| title | Schur property for jump parts of gradient measures |
| topic | Functional Analysis Classical Analysis and ODEs 26B30, 46E35 |
| url | https://arxiv.org/abs/2307.08396 |