DOI: 10.33205/cma.1886631 ISSN: 2651-2939

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

Maria Ines Gareis, Federico Dario Kovac, Fabian Eduardo Levis, Ludmila Zabala
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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 \(0 &lt; q \le 1\). 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 \(\Gamma_{ w,q}\).

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