{"title":"论与奇异超曲面相关的最大算子","authors":"S. E. Usmanov","doi":"10.3103/s1066369x24700051","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>Maximal operators associated with singular hypersurfaces in multidimensional Euclidean spaces are considered. These operators have been proven to be bounded, and an exponent of boundedness in the space of integrable functions has been found for the case when hypersurfaces are given by parametric equations.</p>","PeriodicalId":46110,"journal":{"name":"Russian Mathematics","volume":"126 1","pages":""},"PeriodicalIF":0.5000,"publicationDate":"2024-05-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On Maximal Operators Associated with Singular Hypersurfaces\",\"authors\":\"S. E. Usmanov\",\"doi\":\"10.3103/s1066369x24700051\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<h3 data-test=\\\"abstract-sub-heading\\\">Abstract</h3><p>Maximal operators associated with singular hypersurfaces in multidimensional Euclidean spaces are considered. These operators have been proven to be bounded, and an exponent of boundedness in the space of integrable functions has been found for the case when hypersurfaces are given by parametric equations.</p>\",\"PeriodicalId\":46110,\"journal\":{\"name\":\"Russian Mathematics\",\"volume\":\"126 1\",\"pages\":\"\"},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2024-05-09\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Russian Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.3103/s1066369x24700051\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Russian Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3103/s1066369x24700051","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
On Maximal Operators Associated with Singular Hypersurfaces
Abstract
Maximal operators associated with singular hypersurfaces in multidimensional Euclidean spaces are considered. These operators have been proven to be bounded, and an exponent of boundedness in the space of integrable functions has been found for the case when hypersurfaces are given by parametric equations.
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