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 $L^φ(Ω)$. 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 $L^{ψ^+}(Ω)$. We also get pointwise convergence of this extension, where the Calderón-Zygmund class $t_m^p (x)$ adapted to $L^{ψ^+}(Ω)$ plays an important role.
math.CA↗