加权平方函数不等式

IF 0.8 3区数学 Q2 MATHEMATICS

Publicacions Matematiques Pub Date : 2018-01-01 DOI:10.5565/PUBLMAT6211804

A. Osȩkowski

{"title":"加权平方函数不等式","authors":"A. Osȩkowski","doi":"10.5565/PUBLMAT6211804","DOIUrl":null,"url":null,"abstract":"For an integrable function f on [0, 1)d, let S(f) and M f denote the corresponding dyadic square function and the dyadic maximal function of f, respectively. The paper contains the proofs of the following statements. (i) If w is a dyadic A1 weight on [0, 1)d, then ||S(f)||L1(w) ≤√ 5[w] 1/2 A1 ||M f||L1(w). The exponent 1/2 is shown to be the best possible. (ii) For any p > 1, there are no constants cp, αp epending only on p such that for all dyadic Ap weights w on [0, 1)d, ||S(f)||L1(w) ≤ cp[w] αp Ap ||M f||L1(w).","PeriodicalId":54531,"journal":{"name":"Publicacions Matematiques","volume":"11 1","pages":"75-94"},"PeriodicalIF":0.8000,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"7","resultStr":"{\"title\":\"Weighted square function inequalities\",\"authors\":\"A. Osȩkowski\",\"doi\":\"10.5565/PUBLMAT6211804\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"For an integrable function f on [0, 1)d, let S(f) and M f denote the corresponding dyadic square function and the dyadic maximal function of f, respectively. The paper contains the proofs of the following statements. (i) If w is a dyadic A1 weight on [0, 1)d, then ||S(f)||L1(w) ≤√ 5[w] 1/2 A1 ||M f||L1(w). The exponent 1/2 is shown to be the best possible. (ii) For any p > 1, there are no constants cp, αp epending only on p such that for all dyadic Ap weights w on [0, 1)d, ||S(f)||L1(w) ≤ cp[w] αp Ap ||M f||L1(w).\",\"PeriodicalId\":54531,\"journal\":{\"name\":\"Publicacions Matematiques\",\"volume\":\"11 1\",\"pages\":\"75-94\"},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2018-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"7\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Publicacions Matematiques\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.5565/PUBLMAT6211804\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Publicacions Matematiques","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.5565/PUBLMAT6211804","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 7

摘要

对于可积函数f在[0,1)d上，设S(f)和M f分别表示相应的并进平方函数和f的并进极大函数。本文包含下列陈述的证明。(i)如果w是[0,1)d上的二进A1权值，则||S(f)||L1(w)≤√5[w] 1/2 A1 ||M f||L1(w)。指数1/2是最好的。(ii)对于任何p > 1，不存在仅依赖于p的常数cp， αp，使得对于所有并矢Ap权值w在[0,1)d上，||S(f)| L1(w)≤cp[w] αp Ap |M f| L1(w)。

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

Weighted square function inequalities

For an integrable function f on [0, 1)d, let S(f) and M f denote the corresponding dyadic square function and the dyadic maximal function of f, respectively. The paper contains the proofs of the following statements. (i) If w is a dyadic A1 weight on [0, 1)d, then ||S(f)||L1(w) ≤√ 5[w] 1/2 A1 ||M f||L1(w). The exponent 1/2 is shown to be the best possible. (ii) For any p > 1, there are no constants cp, αp epending only on p such that for all dyadic Ap weights w on [0, 1)d, ||S(f)||L1(w) ≤ cp[w] αp Ap ||M f||L1(w).

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

Publicacions Matematiques 数学-数学

CiteScore

1.60

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Publicacions Matemàtiques is a research mathematical journal published by the Department of Mathematics of the Universitat Autònoma de Barcelona since 1976 (before 1988 named Publicacions de la Secció de Matemàtiques, ISSN: 0210-2978 print, 2014-4369 online). Two issues, constituting a single volume, are published each year. The journal has a large circulation being received by more than two hundred libraries all over the world. It is indexed by Mathematical Reviews, Zentralblatt Math., Science Citation Index, SciSearch®, ISI Alerting Services, COMPUMATH Citation Index®, and it participates in the Euclid Project and JSTOR. Free access is provided to all published papers through the web page. Publicacions Matemàtiques is a non-profit university journal which gives special attention to the authors during the whole editorial process. In 2019, the average time between the reception of a paper and its publication was twenty-two months, and the average time between the acceptance of a paper and its publication was fifteen months. The journal keeps on receiving a large number of submissions, so the authors should be warned that currently only articles with excellent reports can be accepted.