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.File in questo prodotto:
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