改良高斯-魏尔斯特拉斯奇异积分在加权空间中的逼近特性

IF 1.5 3区数学 Q1 MATHEMATICS

Journal of Inequalities and Applications Pub Date : 2024-07-18 DOI:10.1186/s13660-024-03171-9

Abhay Pratap Singh, Uaday Singh

{"title":"改良高斯-魏尔斯特拉斯奇异积分在加权空间中的逼近特性","authors":"Abhay Pratap Singh, Uaday Singh","doi":"10.1186/s13660-024-03171-9","DOIUrl":null,"url":null,"abstract":"Singular integral operators play an important role in approximation theory and harmonic analysis. In this paper, we consider a weighted Lebesgue space $L^{p,w}$ , define a modified Gauss–Weierstrass singular integral on it, and study direct and inverse approximation properties of the operator followed by a Korovkin-type approximation theorem for a function $f\\in L^{p,w}$ . We use the modulus of continuity of the functions to measure the rate of convergence.","PeriodicalId":16088,"journal":{"name":"Journal of Inequalities and Applications","volume":"63 1","pages":""},"PeriodicalIF":1.5000,"publicationDate":"2024-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Approximation properties of a modified Gauss–Weierstrass singular integral in a weighted space\",\"authors\":\"Abhay Pratap Singh, Uaday Singh\",\"doi\":\"10.1186/s13660-024-03171-9\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Singular integral operators play an important role in approximation theory and harmonic analysis. In this paper, we consider a weighted Lebesgue space $L^{p,w}$ , define a modified Gauss–Weierstrass singular integral on it, and study direct and inverse approximation properties of the operator followed by a Korovkin-type approximation theorem for a function $f\\\\in L^{p,w}$ . We use the modulus of continuity of the functions to measure the rate of convergence.\",\"PeriodicalId\":16088,\"journal\":{\"name\":\"Journal of Inequalities and Applications\",\"volume\":\"63 1\",\"pages\":\"\"},\"PeriodicalIF\":1.5000,\"publicationDate\":\"2024-07-18\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Inequalities and Applications\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1186/s13660-024-03171-9\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Inequalities and Applications","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1186/s13660-024-03171-9","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

奇异积分算子在近似理论和谐波分析中发挥着重要作用。在本文中，我们考虑了一个加权的 Lebesgue 空间 $L^{p,w}$，在其上定义了一个修正的高斯-韦尔斯特拉斯奇异积分，并研究了该算子的直接和反向逼近性质，随后针对函数 $f\in L^{p,w}$ 提出了一个 Korovkin 型逼近定理。我们使用函数的连续性模量来衡量收敛速度。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Approximation properties of a modified Gauss–Weierstrass singular integral in a weighted space

Singular integral operators play an important role in approximation theory and harmonic analysis. In this paper, we consider a weighted Lebesgue space $L^{p,w}$ , define a modified Gauss–Weierstrass singular integral on it, and study direct and inverse approximation properties of the operator followed by a Korovkin-type approximation theorem for a function $f\in L^{p,w}$ . We use the modulus of continuity of the functions to measure the rate of convergence.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Journal of Inequalities and Applications 数学-数学

自引率

6.20%

发文量

136

期刊介绍： The aim of this journal is to provide a multi-disciplinary forum of discussion in mathematics and its applications in which the essentiality of inequalities is highlighted. This Journal accepts high quality articles containing original research results and survey articles of exceptional merit. Subject matters should be strongly related to inequalities, such as, but not restricted to, the following: inequalities in analysis, inequalities in approximation theory, inequalities in combinatorics, inequalities in economics, inequalities in geometry, inequalities in mechanics, inequalities in optimization, inequalities in stochastic analysis and applications.