English

On the Embedding of $BV$ Space into Besov-Orlicz Space

Functional Analysis 2021-10-26 v1

Abstract

We give a sufficient (and, in the case of a compact domain, a necessary) condition for the embedding of Sobolev space of functions with integrable gradient into Besov-Orlicz spaces to be bounded. The condition has a form of a simple integral inequality involving Young and weight functions. We provide an example with Matuszewska-Orlicz indices of involved Orlicz norm equal to one. The main tool is the molecular decomposition of functions from a BV space.

Keywords

Cite

@article{arxiv.2110.12480,
  title  = {On the Embedding of $BV$ Space into Besov-Orlicz Space},
  author = {Aleksander Pawlewicz and Michał Wojciechowski},
  journal= {arXiv preprint arXiv:2110.12480},
  year   = {2021}
}

Comments

15 pages