Fractional Sobolev Spaces and Functions of Bounded Variation
Abstract
We investigate the 1D Riemann-Liouville fractional derivative focusing on the connections with fractional Sobolev spaces, the space $BV$ of functions of bounded variation, whose derivatives are not functions but measures and the space $SBV$, say the space of bounded variation functions whose derivative has no Cantor part. We prove that $SBV$ is included in $W^{s,1} $ for every $s \in (0,1)$ while the result remains open for $BV$. We study examples and address open questions.
- Publication:
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arXiv e-prints
- Pub Date:
- March 2016
- DOI:
- 10.48550/arXiv.1603.05033
- arXiv:
- arXiv:1603.05033
- Bibcode:
- 2016arXiv160305033B
- Keywords:
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- Mathematics - Optimization and Control;
- Mathematics - Functional Analysis
- E-Print:
- Fractional Calculus and Applied Analysis, 20(4), pp. 936-962. Retrieved 20 Jan. 2018, from doi:10.1515/fca-2017-0049