2004/09/01 by Sorina Barza, Anna Kaminska, Barza, Sorina +5
Mathematics · #46B25 #46E30 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA) #math.CA #math.FA #msc:46B25 #msc:46E30
paper · pdf · doi:10.48550/arxiv.math/0409018
16 pages
arxiv created 2004/09/01 · arxiv updated 2009/12/01
In the last decade, the problem of characterizing the normability of the weighted Lorentz spaces has been completely solved (\citeSa, \citeCaSoA). 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.