The best constant approximant operators in Lorentz spaces Γp,w and their applications

Abstract

In the present article we extend the best constant approximant operator from Lorentz spaces Γ p,w to Γ p−1,w for any 1 < p < ∞ and w ≥ 0 a locally integrable weight function, and from Γ 1,w to the space of all measurable functions L 0 . Then we establish several properties of the extended best constant approximant operator and finally, we prove a generalized version of the Lebesgue Differentiation Theorem in L 0 .