Relative Rearrangement Method for Estimating Dual Norms

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.
Anno
2009
Tipo pubblicazione
Altri Autori
Fiorenza A.; Rakotoson J.M.; Zitouni L.
Editore
[Dept. of Mathematics], Indiana University
Rivista
Indiana University mathematics journal (Online)