Quantitative estimates and near-best properties of extended best approximation in $\Gamma_{w,q}$ spaces for $0 < q \le 1$

Source abstract

This article investigates the extended best polynomial approximation operator, defined on the space of measurable functions, within the setting of Lorentz Gamma spaces $\Gamma_{ w,q}$ for $0 < q \le 1$. We derive quantitative estimates for extended best approximations and the outer operator quasi-norm. As a consequence, we show that extended best approximations in $\Gamma_{ w,1}$ are near-best approximations in $\Gamma_{ w,q}$.