Embeddings and duality theorems for weak classical lorentz spaces

Abstract

We characterize the weight functions u, v, w on (0, ∞) such that (∫0∞ f*(t)qw(t) dt) 1/q ≤ C sup fu** (t)v(t), tε(0,∞) where fu**(t) := (∫ 0t u(s) ds)-1 ∫0t f* (s)u(s) ds. As an application we present a new simple characterization of the associate space to the space Γ∞(ν), determined by the norm ∥f∥Γ∞(ν) = sup f** (t)ν(t), tε(0, ∞) where f**(t):= 1/t ∫0t f* (s) ds. © Canadian Mathematical Society 2006.