Relative rearrangement method for estimating dual norms A. FiorenzaJ. RakotosonL. Zitouni 46E3046D35Banach function spacesrelative rearrangementmonotone rearrangementweightssmall and grand Lebesgue spaces The Generalized-$\Gamma$-Space $\G\Gamma(p,m,w)$ 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 $\Gamma$-space $\G\Gamma(p,m,w)$ 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 $\G\Gamma(p,m,w)$ is reflexive under the conditions that $m>1$ and $p\geq2$. Indiana University Mathematics Journal 2009 text pdf 10.1512/iumj.2009.58.3580 10.1512/iumj.2009.58.3580 en Indiana Univ. Math. J. 58 (2009) 1127 - 1150 state-of-the-art mathematics http://iumj.org/access/