某些巴拿赫函数空间的平滑度模量

Pub Date : 2023-12-11 DOI:10.1007/s11253-023-02253-z

Ramazan Akgün

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引用次数: 0

摘要

基于斯特克洛夫算子，我们考虑了某些巴拿赫函数空间中函数的平滑度模量，它可能不是平移不变的，并确定了它的主要性质。借助杰克逊型直接定理和三角函数逼近的逆定理，我们获得了该 Lipschitz 类的构造性特征。作为应用，我们举了几个相关（加权）函数空间的例子。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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A Modulus of Smoothness for Some Banach Function Spaces

Based on the Steklov operator, we consider a modulus of smoothness for functions in some Banach function spaces, which can be not translation invariant, and establish its main properties. A constructive characterization of the Lipschitz class is obtained with the help of the Jackson-type direct theorem and the inverse theorem on trigonometric approximation. As an application, we present several examples of related (weighted) function spaces.

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