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The Generalized- ? -Space G? (p, m, w) contains many classical rearrangement invariant spaces. Here we shall study its associate space and we shall estimate its associate norm. In particular, we characterize all optimal functions u achieving the associate norm of Generalized ? -space G ? (p, m, w) when it is reflexive. For the purpose, we use the notion of relative rearrangement and new additional results on this concept. Moreover, we prove that the space G? (p, m, w) is reflexive under the conditions that m > 1 and p >= 2.

Relative Rearrangement Method for Estimating Dual Norms

Fiorenza A;
2009

Abstract

The Generalized- ? -Space G? (p, m, w) contains many classical rearrangement invariant spaces. Here we shall study its associate space and we shall estimate its associate norm. In particular, we characterize all optimal functions u achieving the associate norm of Generalized ? -space G ? (p, m, w) when it is reflexive. For the purpose, we use the notion of relative rearrangement and new additional results on this concept. Moreover, we prove that the space G? (p, m, w) is reflexive under the conditions that m > 1 and p >= 2.
2009
Istituto Applicazioni del Calcolo ''Mauro Picone''
Inglese
WOS:000268360000005
58
3
1127
1149
23
2-s2.0-69549131382
http://www.iumj.indiana.edu
Sì, ma tipo non specificato
Generalized Lorentz Spaces
small Lebesgue spaces
Banach Function Spaces
relative rearrangement method
Lagrange multipliers for multiconstraint problems
This paper represents the endpoint of a series of papers started with the introduction of the small Lebesgue spaces, made by the first author, in a paper published in Collectanea Mathematica (2000). After a study realized in papers published in journals of intermediate level, this paper has been published in a journal of high level, because the generalization constructed in these pages puts these spaces in the framework of the family of the Lorentz spaces. The delicate estimate of the dual norm, which required high work already in the case of the small Lebesgue spaces, here is obtained with the use of the relative rearrangement method.
3
info:eu-repo/semantics/article
262
Fiorenza, A; Rakotoson, Jm; Zitouni, L
01 Contributo su Rivista::01.01 Articolo in rivista
none
01.01 Articolo in rivista
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.14243/161107
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