A Lebesgue Type Differentiation Theorem for Best Approximations by Constants in Orlicz Spaces
A Lebesgue Type Differentiation Theorem for Best Approximations by Constants in Orlicz Spaces
The best approximation operator by constants is extended from an Orlicz space $L^{\varphi}({\mathbb R}^m)$ to the space $L^{\varphi '} ({\mathbb R}^m),$ and some properties of this extended operator are established. Let $f_{\varepsilon}(x)$ be any best approximation of $f\in L^{\varphi '} ({\mathbb R}^m)$ on a suitable set $\beta_{\varepsilon} (X) \subset \mathbb{ …