This article investigates polynomial approximations in Lorentz Gamma spaces, uncovering their best properties.
This article investigates the extended best polynomial approximation operator, defined on the space of measurable functions, within the setting of Lorentz Gamma spaces \(Γw,q\) for \(0 < q ≤ 1\). We derive quantitative estimates for extended best approximations and the outer operator quasi-norm. As a consequence, we show that extended best approximations in \(Γw,1\) are near-best approximations in \(Γw,q\).
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Gareis et al. (2026) studied this question.
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