Schur property for jump parts of gradient measures

Krystian Kazaniecki; Anton Tselishchev; Michał Wojciechowski

Schur property for jump parts of gradient measures

Functional Analysis 2024-07-01 v2 Classical Analysis and ODEs

Authors: Krystian Kazaniecki , Anton Tselishchev , Michał Wojciechowski

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 $W^{1,1}.$

Keywords

bounded variation sbv space weakly null sequences jump part gradient measures dunford-pettis property sobolev space

Cite

@article{arxiv.2307.08396,
  title  = {Schur property for jump parts of gradient measures},
  author = {Krystian Kazaniecki and Anton Tselishchev and Michał Wojciechowski},
  journal= {arXiv preprint arXiv:2307.08396},
  year   = {2024}
}

Comments

18 pages; the presentation is sufficiently improved in v2

Schur property for jump parts of gradient measures

Abstract

Keywords

Cite

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