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AI Summary & Key Takeaways
AI Insight⚡ TL;DR(Too Long; Didn't Read)
As a corollary some results on the constructive characterization problems in the generalized Lipschitz classes are presented.
📌 3 Key Takeaways
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Objective & Hypothesis:Let $G\subset \mathbb{C}$ be a bounded Jordan domain with a rectifiable Dini-smooth boundary $\Gamma $ and let $G^{-}:=ext~ \Gamma $.
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Key Findings & Data:In terms of the higher order modulus of smoothness the direct and inverse problems of approximation theory in the variable exponent Smirnov classes $E^{p(\cdot )}(G)$ and $E^{p(\cdot )}(G^{-})$ \ are investigated.
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Conclusion & Impact:As a corollary some results on the constructive characterization problems in the generalized Lipschitz classes are presented.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Variable exponent Smirnov classes · direct and inverse theorems · Faber series
Abstract
Let $G\subset \mathbb{C}$ be a bounded Jordan domain with a rectifiable Dini-smooth boundary $\Gamma $ and let $G^{-}:=ext~ \Gamma $. In terms of the higher order modulus of smoothness the direct and inverse problems of approximation theory in the variable exponent Smirnov classes $E^{p(\cdot )}(G)$ and $E^{p(\cdot )}(G^{-})$ \ are investigated. Moreover, the Marcinkiewicz and Littlewood-Paley type theorems are proved. As a corollary some results on the constructive characterization problems in the generalized Lipschitz classes are presented.
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Cite This Article
ISRAFILOV, D., TESTİCİ, A. (2022). Multiplier and approximation theorems in Smirnov classes with variable exponent. Turkish Journal of Mathematics, Cilt: 42 - Sayı: 3, 1442–1456. https://ajindex.com/articles/607813