Multidimensional rearrangement and Lorentz spaces

Authors: Sorina Barza¹; Lars-Erik Persson²; Javier Soria³

Source: Acta Mathematica Hungarica, Volume 104, Number 3, 2004 , pp. 203-224(22)

Publisher: Springer

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Abstract:

We define a multidimensional rearrangement, which is related to classical inequalities for functions that are monotone in each variable. We prove the main measure theoretical results of the new theory and characterize the functional properties of the associated weighted Lorentz spaces.

Keywords: rearrangement; function spaces; Lorentz spaces; monotone functions; weighted inequalities

Document Type: Research article

DOI: http://dx.doi.org/10.1023/B:AMHU.0000036283.75990.a2

Affiliations: 1: Department of Mathematics, Karlstad University S-65188 Karlstad, Sweden, Email: sorina.barza@kau.se 2: Department of Mathematics, Luleå University S-97187 Luleå, Sweden, Email: larserik@sm.luth.se 3: Department of Applied Mathematics and Analysis, University of Barcelona E-08071 Barcelona, Spain, Email: soria@mat.ub.es

Publication date: 2004-01-01