Extension of the Best Constant Approximation Operator in Orlicz Spaces

Abstract

In this article we deal with the best φ-approximation operator by constants extended from an Orlicz space Lφ(Ω) to the space Lψ+ (Ω) where ψ+ denotes the right derivative of the function φ. We obtain pointwise convergence for a suitable class of functions. Also we consider a maximal operator which allows as to get modular convergence for a specific class of Orlicz spaces.