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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 tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
Department of Applied Mathematics and Analysis, University of Barcelona.
2006 (engelsk)Inngår i: Positivity (Dordrecht), ISSN 1385-1292, E-ISSN 1572-9281, Vol. 10, nr 3, s. 539-554Artikkel i tidsskrift (Fagfellevurdert) 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.

sted, utgiver, år, opplag, sider
2006. Vol. 10, nr 3, s. 539-554
HSV kategori
Forskningsprogram
Matematik
Identifikatorer
URN: urn:nbn:se:ltu:diva-2647DOI: 10.1007/s11117-005-0004-3ISI: 000239393400007Scopus ID: 2-s2.0-33746776749Lokal ID: 04d30d60-a169-11db-8975-000ea68e967bOAI: oai:DiVA.org:ltu-2647DiVA, id: diva2:975500
Merknad
Validerad; 2006; 20070111 (evan)Tilgjengelig fra: 2016-09-29 Laget: 2016-09-29 Sist oppdatert: 2018-07-10bibliografisk kontrollert

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