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On Fubini type property in Lorentz spaces
Karlstad University, Faculty of Technology and Science, Department of Mathematics. (Matematik)ORCID iD: 0000-0001-5459-0796
2012 (English)In: Recent Advances in Harmonic Analysis and Applications / [ed] Bilyk, D., New York: Springer, 2012, p. 171-179Chapter in book (Refereed)
Abstract [en]

We study Fubini-type property for Lorentz spaces L p,r (R 2 ) . This problem is twofold. First we assume that all linear sections of a function f in directions of coordinate axes belong to L p,r (R) , and their one-dimensional Lp, r-norms belong to L p,r (R). We show that for pr it does not imply that f∈L p,r (R 2 ) (this complements one result by Cwikel). Conversely, we assume that f∈L p,r (R 2 ) , and we show that then for r < p almost all linear sections of f belong to L p,r (R) , but for p < r all linear sections may have infinite one-dimensional Lp, r-norms

Place, publisher, year, edition, pages
New York: Springer, 2012. p. 171-179
Series
Springer Proceedings in Mathematics and Statistics, ISSN 2194-1009, E-ISSN 1024003 ; 25
National Category
Mathematical Analysis
Identifiers
URN: urn:nbn:se:kau:diva-15785DOI: 10.1007/978-1-4614-4565-4_16ISBN: 978-1-4614-4564-7 (print)ISBN: 978-1-4614-4565-4 (print)OAI: oai:DiVA.org:kau-15785DiVA, id: diva2:571977
Available from: 2012-11-26 Created: 2012-11-26 Last updated: 2018-07-17Bibliographically approved

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Kolyada, Viktor

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Citation style
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