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arXiv · 2402.17048

Extension of the Best Polynomial Operator in Generalized Orlicz spaces

Sonia Acinas·Sergio Favier·Rosa Lorenzo
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Abstract

In this paper, we consider the best multivalued polynomial approximation operator for functions in an Orlicz Space $L^{\varphi}(\Omega)$. We obtain its characterization involving $\psi^-$ and $\psi^+$, which are the left and right derivatives functions of $\varphi$. And then, we extend the operator to $L^{\psi^+}(\Omega)$. We also get pointwise convergence of this extension, where the Calder\'on-Zygmund class $t_m^p (x)$ adapted to $L^{\psi^+}(\Omega)$ plays an important role.

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Sonia Acinas, Sergio Favier, Rosa Lorenzo. 2024-02-26. Extension of the Best Polynomial Operator in Generalized Orlicz spaces. https://doi.org/10.1016/j.jat.2025.106174

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