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Accessible Unlicensed Requires Authentication Published by De Gruyter August 8, 2017

Fractional sobolev spaces and functions of bounded variation of one variable

Maïtine Bergounioux, Antonio Leaci, Giacomo Nardi and Franco Tomarelli

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 Ws,1 for every s ∈ (0, 1) while the result remains open for BV. We study examples and address open questions.

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Received: 2016-7-27
Revised: 2017-6-20
Published Online: 2017-8-8
Published in Print: 2017-8-28

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