Extension of the Best Polynomial Operator in Generalized Orlicz spaces
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866913859788341248 |
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| author | Acinas, Sonia Favier, Sergio Lorenzo, Rosa |
| author_facet | Acinas, Sonia Favier, Sergio Lorenzo, Rosa |
| contents | In this paper, we consider the best multivalued polynomial approximation operator for functions in an Orlicz Space $L^φ(Ω)$. We obtain its characterization involving $ψ^-$ and $ψ^+$, which are the left and right derivatives functions of $φ$. And then, we extend the operator to $L^{ψ^+}(Ω)$. We also get pointwise convergence of this extension, where the Calderón-Zygmund class $t_m^p (x)$ adapted to $L^{ψ^+}(Ω)$ plays an important role. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_17048 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Extension of the Best Polynomial Operator in Generalized Orlicz spaces Acinas, Sonia Favier, Sergio Lorenzo, Rosa Classical Analysis and ODEs 41A10 In this paper, we consider the best multivalued polynomial approximation operator for functions in an Orlicz Space $L^φ(Ω)$. We obtain its characterization involving $ψ^-$ and $ψ^+$, which are the left and right derivatives functions of $φ$. And then, we extend the operator to $L^{ψ^+}(Ω)$. We also get pointwise convergence of this extension, where the Calderón-Zygmund class $t_m^p (x)$ adapted to $L^{ψ^+}(Ω)$ plays an important role. |
| title | Extension of the Best Polynomial Operator in Generalized Orlicz spaces |
| topic | Classical Analysis and ODEs 41A10 |
| url | https://arxiv.org/abs/2402.17048 |