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arXiv · 2307.08396

Schur property for jump parts of gradient measures

Krystian Kazaniecki·Anton Tselishchev·Michał Wojciechowski
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Abstract

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 $W^{1,1}.$

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Krystian Kazaniecki, Anton Tselishchev, Michał Wojciechowski. 2023-07-17. Schur property for jump parts of gradient measures. https://arxiv.org/abs/2307.08396

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