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