Norms of Maximal Functions between Generalized and Classical Lorentz Spaces

Abstract

The aim of the paper is to find the norm of the generalized maximal operator M ϕ,Λ α (b) , defined for all measurable functions f on R n , with 0 < α < ∞ and functions b, ϕ : (0, ∞) → (0, ∞), byQ∋x t 0 b(s) ds satisfies 0 < B(t) < ∞ for every t ∈ (0, ∞).