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

Kopaliani, Tengiz; Samashvili, Nino; Zviadadze, Shalva

doi:10.1215/20088752-3505953

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2022

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“…In 2011, Cuenya [5] extended the best polynomial approximation operator from 𝐿 𝑝 to 𝐿 𝑝−1 , while similar problems concerning the extensions of the best polynomial approximations in Orlicz spaces have been investigated by Acinas, Favier and Zo in the papers [1,2]. Similar results in variable exponent Lebesgue spaces have appeared in [13].…”

Section: Introductionmentioning

confidence: 99%

Extended best polynomial approximation operator in Orlicz–Lorentz spaces

Ferreyra

Gareis

Levis

2022

Mathematische Nachrichten

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In this article, we consider the best polynomial approximation operator defined on an Orlicz-Lorentz space Λ 𝑤,𝜙 generated by an Orlicz function 𝜙 and a nonnegative continuous weight function 𝑤. Then we extend the best polynomial approximation operator from Λ 𝑤,𝜙 to Λ 𝑤,𝜙 ′ , where 𝜙 ′ is the derivative function of 𝜙. In addition, we establish some properties of the extended best polynomial approximation operator.

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Section: Introductionmentioning

confidence: 99%