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On fractional smoothness of functions related to p-variation
Karlstad University, Faculty of Technology and Science, Department of Mathematics. (Matematik)ORCID iD: 0000-0002-1752-1211
2013 (English)In: Mathematical Inequalities & Applications, ISSN 1331-4343, E-ISSN 1848-9966, Vol. 16, no 1, p. 21-39Article in journal (Refereed) Published
Abstract [en]

This paper is concerned with the study of two functionals of variational type - the Riesz type generalized variation v_{p,\alpha}(f) (1<p<\infty, 0\le\alpha\le1-1/p) and the moduli of p-continuity \omega_{1-1/p}(f;d). These functionals generate scales of spaces connecting the class of functions of bounded p-variation and the Sobolev space W_p^1. Some limiting relations in these scales are proved. Sharp estimates of v_{p,\alpha}(f) in terms of \omega_{1-1/p}(f;d) are obtained.

Place, publisher, year, edition, pages
Zagreb: Element d.o.o. publishing house , 2013. Vol. 16, no 1, p. 21-39
Keywords [en]
functions of bounded p-variation, generalized variations, optimal constants, function spaces
National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:kau:diva-15100DOI: 10.7153/mia-16-02ISI: 000317599800002OAI: oai:DiVA.org:kau-15100DiVA, id: diva2:558761
Available from: 2012-10-05 Created: 2012-10-05 Last updated: 2019-07-12Bibliographically approved

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Lind, Martin

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