Let \({ G\subset {\mathbb {C}} }\) be a Jordan domain with rectifiable Dini smooth boundary \(\varGamma \). In this work, we investigate approximation properties of matrix transforms constructed via Faber series in weighted Smirnov classes with variable exponent. Moreover, direct and inverse theorems of approximation theory in weighted Smirnov classes with variable exponent are proved and some results related to constructive characterization in generalized Lipschitz classes are obtained.

中文翻译：

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可变指数加权Smirnov类中的逼近理论的一些定理

令\（{G \ subset {\ mathbb {C}}} \）为具有可校正Dini光滑边界\（\ varGamma \）的Jordan域。在这项工作中，我们研究在可变指数加权Smirnov类中通过Faber级数构造的矩阵变换的近似性质。此外，证明了可变指数加权Smirnov类中逼近理论的直接定理和逆定理，并获得了与广义Lipschitz类的构造表征有关的一些结果。