Extension of the Best Polynomial Operator in Generalized Orlicz spaces

In this paper, we consider the best multivalued polynomial approximation operator for functions in an Orlicz Space Lφ(Ω). We obtain its characterization involving ψ⁻ and ψ⁺, which are the left and right derivatives functions of φ. And then, we extend the operator to Lψ⁺(Ω). We also get pointwise convergence of this extension, where the Calder\'on-Zygmund class tₘᵖ (x) adapted to Lψ⁺(Ω) plays an important role.