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

FRACTIONAL SOBOLEV SPACES AND FUNCTIONS OF BOUNDED VARIATION OF ONE VARIABLE

TOMARELLI, FRANCO
2017-01-01

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 ∈ (0, 1) while the result remains open for BV . We study examples and address open questions.
2017
fractional calculus
Riemann-Liouville derivative
bounded variation functions
Marchaud derivative
Sobolev spaces
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11311/1031258
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