多变量抽样Kantorovich算子：Orlicz空间中的定量估计

IF 1.1 Q1 MATHEMATICS

Constructive Mathematical Analysis Pub Date : 2021-02-16 DOI:10.33205/CMA.876890

L. Angeloni, N. Çetin, D. Costarelli, A. R. Sambucini, G. Vinti

{"title":"多变量抽样Kantorovich算子：Orlicz空间中的定量估计","authors":"L. Angeloni, N. Çetin, D. Costarelli, A. R. Sambucini, G. Vinti","doi":"10.33205/CMA.876890","DOIUrl":null,"url":null,"abstract":"In this paper, we establish a quantitative estimate for multivariate sampling Kantorovich operators by means of the modulus of continuity in the general setting of Orlicz spaces. As a consequence, the qualitative order of convergence can be obtained, in case of functions belonging to suitable Lipschitz classes. In the particular instance of L^p-spaces, using a direct approach, we obtain a sharper estimate than that one that can be deduced from the general case.","PeriodicalId":36038,"journal":{"name":"Constructive Mathematical Analysis","volume":null,"pages":null},"PeriodicalIF":1.1000,"publicationDate":"2021-02-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"10","resultStr":"{\"title\":\"Multivariate sampling Kantorovich operators: quantitative estimates in Orlicz spaces\",\"authors\":\"L. Angeloni, N. Çetin, D. Costarelli, A. R. Sambucini, G. Vinti\",\"doi\":\"10.33205/CMA.876890\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we establish a quantitative estimate for multivariate sampling Kantorovich operators by means of the modulus of continuity in the general setting of Orlicz spaces. As a consequence, the qualitative order of convergence can be obtained, in case of functions belonging to suitable Lipschitz classes. In the particular instance of L^p-spaces, using a direct approach, we obtain a sharper estimate than that one that can be deduced from the general case.\",\"PeriodicalId\":36038,\"journal\":{\"name\":\"Constructive Mathematical Analysis\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.1000,\"publicationDate\":\"2021-02-16\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"10\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Constructive Mathematical Analysis\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.33205/CMA.876890\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Constructive Mathematical Analysis","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.33205/CMA.876890","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 10

摘要

本文利用Orlicz空间的一般设置中的连续模，建立了多元采样Kantorovich算子的定量估计。因此，在函数属于合适的Lipschitz类的情况下，可以获得收敛的定性阶。在L^p-空间的特定例子中，使用直接方法，我们获得了比从一般情况中推导出的估计更清晰的估计。

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

Multivariate sampling Kantorovich operators: quantitative estimates in Orlicz spaces

In this paper, we establish a quantitative estimate for multivariate sampling Kantorovich operators by means of the modulus of continuity in the general setting of Orlicz spaces. As a consequence, the qualitative order of convergence can be obtained, in case of functions belonging to suitable Lipschitz classes. In the particular instance of L^p-spaces, using a direct approach, we obtain a sharper estimate than that one that can be deduced from the general case.

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

Constructive Mathematical Analysis Mathematics-Analysis

CiteScore

2.40

自引率

0.00%

发文量

审稿时长

6 weeks