Extension of the best polynomial approximation operator in variable exponent Lebesgue spaces

Abstract

Let $\Omega$ be a bounded measurable set in ${\mathbb{R}}^n$. The best polynomial approximation operator was recently extended by Cuenya from $L^p$ to $L^{p-1}$.

In this paper, we extend the operator of the best polynomial approximation from $L^{p(\cdot )}(\Omega )$ to the space $L^{p(\cdot )-1}(\Omega )$.