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Mixed Norm and Multidimensional Lorentz Spaces |
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| Authors: | Sorina Barza Anna Kamińska Lars-Erik Persson Javier Soria |
| Affiliation: | 1. Dept. of Mathematics, Physics and Eng. Sciences, Karlstad University, SE-65188, Karlstad, Sweden 2. Dept. of Mathematical Sciences, The University of Memphis, Memphis, TN, 38152-3240, USA 3. Dept. of Mathematics, Lule? University of Technology, SE-97187, Lule?, Sweden 4. Dept. Appl. Math. and Analysis, University of Barcelona, E-08007, Barcelona, Spain |
| Abstract: | 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. Research partially supported by KAW 2000.0048 and STINT KU 2002-4025. Research partially supported by Grants MTM2004-02299, 2005SGR00556 and The Swedish Research Council no. 624-2003-571. |
| Keywords: | 46E30 46B25 |
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