Hölder type inequalities in Lorentz spaces

Abstract

We study optimal Hölder type inequalities for the Lorentz spaces Lp,s(R, μ), in the range 1 < p < ∞, 1 ≤ s ≤ ∞, for both the maximal and the dual norms. These estimates also give sharp results for the corresponding associate norms. © 2009 Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag.