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arXiv · 2110.12480

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

Aleksander Pawlewicz·Michał Wojciechowski
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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.

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Aleksander Pawlewicz, Michał Wojciechowski. 2021-10-24. On the Embedding of $BV$ Space into Besov-Orlicz Space. https://arxiv.org/abs/2110.12480

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