Riemann–Liouville Fractional Sobolev and Bounded Variation Spaces

Axioms

Antonio Leaci¹  Franco Tomarelli² 

[1] Dipartimento di Matematica e Fisica “Ennio De Giorgi”, Università del Salento, 73100 Lecce, Italy;Politecnico di Milano, Dipartimento di Matematica, 20133 Milan, Italy;

关键词: fractional derivatives;    distributional derivatives;    Sobolev spaces;    bounded variation functions;    embeddings;    compactness;   

DOI  :  10.3390/axioms11010030

来源: DOAJ

【 摘 要 】

We establish some properties of the bilateral Riemann–Liouville fractional derivative $D^s$. We set the notation, and study the associated Sobolev spaces of fractional order s, denoted by $W^{s,1}(a,b)$, and the fractional bounded variation spaces of fractional order s, denoted by $B{V}^s(a,b)$. Examples, embeddings and compactness properties related to these spaces are addressed, aiming to set a functional framework suitable for fractional variational models for image analysis.

【 授权许可】

Unknown