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Mixed norm and multidimensional Lorentz spaces
Department of Mathematics, Physics and Engineering Sciences, Karlstad University.
Department of Mathematical Sciences, University of Memphis.
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
Department of Applied Mathematics and Analysis, University of Barcelona.
2006 (English)In: Positivity (Dordrecht), ISSN 1385-1292, E-ISSN 1572-9281, Vol. 10, no 3, p. 539-554Article in journal (Refereed) Published
Abstract [en]

In the last decade, the problem of characterizing the normability of the weighted Lorentz spaces has been completely solved ([16], [7]). However, the question for multidimensional Lorentz spaces is still open. In this paper, we consider weights of product type, and give necessary and sufficient conditions for the Lorentz spaces, defined with respect to the two-dimensional decreasing rearrangement, to be normable. To this end, it is also useful to study the mixed norm Lorentz spaces. Finally, we prove embeddings between all the classical, multidimensional, and mixed norm Lorentz spaces.

Place, publisher, year, edition, pages
2006. Vol. 10, no 3, p. 539-554
National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:ltu:diva-2647DOI: 10.1007/s11117-005-0004-3ISI: 000239393400007Scopus ID: 2-s2.0-33746776749Local ID: 04d30d60-a169-11db-8975-000ea68e967bOAI: oai:DiVA.org:ltu-2647DiVA, id: diva2:975500
Note
Validerad; 2006; 20070111 (evan)Available from: 2016-09-29 Created: 2016-09-29 Last updated: 2018-07-10Bibliographically approved

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Persson, Lars-Erik

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