Riemann-Liouville Fractional Sobolev and Bounded Variation Spaces

被引：3

作者：

Leaci, Antonio ^{[1
]}

Tomarelli, Franco ^{[2
]}

机构：

[1] Univ Salento, Dipartimento Matemat & Fis Ennio De Giorgi, I-73100 Lecce, Italy

[2] Politecn Milan, Dipartimento Matemat, I-20133 Milan, Italy

来源：

AXIOMS | 2022年 / 11卷 / 01期

关键词：

fractional derivatives; distributional derivatives; Sobolev spaces; bounded variation functions; embeddings; compactness; calculus of variations; Abel equation; BLAKE; EQUATIONS;

D O I：

10.3390/axioms11010030

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

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,W-1(a,b), and the fractional bounded variation spaces of fractional order s, denoted by BVs(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.

引用

页数：31

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