索博列夫空间重新审视

IF 0.6 4区数学 Q3 MATHEMATICS

Rendiconti Lincei-Matematica e Applicazioni Pub Date : 2022-02-03 DOI:10.4171/RLM/976

H. Brezis, A. Seeger, Jean Van Schaftingen, Po-Lam Yung

{"title":"索博列夫空间重新审视","authors":"H. Brezis, A. Seeger, Jean Van Schaftingen, Po-Lam Yung","doi":"10.4171/RLM/976","DOIUrl":null,"url":null,"abstract":". We describe a recent, one-parameter family of characterizations of Sobolev and BV functions on R n , using sizes of superlevel sets of suitable difference quotients. This provides an alternative point of view to the BBM formula by Bourgain, Brezis and Mironescu, and complements in the case of BV some results of Cohen, Dahmen, Daubechies and DeVore about the sizes of wavelet coefficients of such functions. An application towards Gagliardo-Nirenberg interpolation inequalities is then given. We also establish a related one-parameter family of formulae for the L p norm of functions in L p ( R n ) .","PeriodicalId":54497,"journal":{"name":"Rendiconti Lincei-Matematica e Applicazioni","volume":null,"pages":null},"PeriodicalIF":0.6000,"publicationDate":"2022-02-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"12","resultStr":"{\"title\":\"Sobolev spaces revisited\",\"authors\":\"H. Brezis, A. Seeger, Jean Van Schaftingen, Po-Lam Yung\",\"doi\":\"10.4171/RLM/976\",\"DOIUrl\":null,\"url\":null,\"abstract\":\". We describe a recent, one-parameter family of characterizations of Sobolev and BV functions on R n , using sizes of superlevel sets of suitable difference quotients. This provides an alternative point of view to the BBM formula by Bourgain, Brezis and Mironescu, and complements in the case of BV some results of Cohen, Dahmen, Daubechies and DeVore about the sizes of wavelet coefficients of such functions. An application towards Gagliardo-Nirenberg interpolation inequalities is then given. We also establish a related one-parameter family of formulae for the L p norm of functions in L p ( R n ) .\",\"PeriodicalId\":54497,\"journal\":{\"name\":\"Rendiconti Lincei-Matematica e Applicazioni\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2022-02-03\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"12\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Rendiconti Lincei-Matematica e Applicazioni\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.4171/RLM/976\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Rendiconti Lincei-Matematica e Applicazioni","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4171/RLM/976","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 12

摘要

．利用合适差商的超水平集的大小，我们描述了R n上Sobolev函数和BV函数的一个最新的单参数表征族。这为Bourgain, Brezis和Mironescu的BBM公式提供了另一种观点，并在BV的情况下补充了Cohen, Dahmen, Daubechies和DeVore关于这类函数的小波系数大小的一些结果。然后给出了对Gagliardo-Nirenberg插值不等式的一个应用。我们还建立了有关的L p (R n)中函数的L p范数的单参数族公式。

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

Sobolev spaces revisited

. We describe a recent, one-parameter family of characterizations of Sobolev and BV functions on R n , using sizes of superlevel sets of suitable difference quotients. This provides an alternative point of view to the BBM formula by Bourgain, Brezis and Mironescu, and complements in the case of BV some results of Cohen, Dahmen, Daubechies and DeVore about the sizes of wavelet coefficients of such functions. An application towards Gagliardo-Nirenberg interpolation inequalities is then given. We also establish a related one-parameter family of formulae for the L p norm of functions in L p ( R n ) .

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

Rendiconti Lincei-Matematica e Applicazioni MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

1.30

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： The journal is dedicated to the publication of high-quality peer-reviewed surveys, research papers and preliminary announcements of important results from all fields of mathematics and its applications.