{"title":"双曲空间中的分数极大算子","authors":"Gonzalo Ibañez-Firnkorn, Emanuel Ramadori","doi":"10.1016/j.jmaa.2024.129079","DOIUrl":null,"url":null,"abstract":"<div><div>In this article, we introduce the fractional maximal operator on the Hyperbolic space, a non-doubling measure space, and study its weighted boundedness. Motivated by the weighted boundedness of the Hardy-Littlewood maximal studied by Antezana and Ombrosi in <span><span>[1]</span></span>, we give conditions for the weak type and strong type estimate for fractional maximal. Also, we present examples of weights for which the fractional maximal operator satisfies weak type <span><math><mo>(</mo><mi>p</mi><mo>,</mo><mi>q</mi><mo>)</mo></math></span> inequality but strong type <span><math><mo>(</mo><mi>p</mi><mo>,</mo><mi>q</mi><mo>)</mo></math></span> inequality fails.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"544 2","pages":"Article 129079"},"PeriodicalIF":1.2000,"publicationDate":"2024-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Fractional maximal operator in hyperbolic spaces\",\"authors\":\"Gonzalo Ibañez-Firnkorn, Emanuel Ramadori\",\"doi\":\"10.1016/j.jmaa.2024.129079\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>In this article, we introduce the fractional maximal operator on the Hyperbolic space, a non-doubling measure space, and study its weighted boundedness. Motivated by the weighted boundedness of the Hardy-Littlewood maximal studied by Antezana and Ombrosi in <span><span>[1]</span></span>, we give conditions for the weak type and strong type estimate for fractional maximal. Also, we present examples of weights for which the fractional maximal operator satisfies weak type <span><math><mo>(</mo><mi>p</mi><mo>,</mo><mi>q</mi><mo>)</mo></math></span> inequality but strong type <span><math><mo>(</mo><mi>p</mi><mo>,</mo><mi>q</mi><mo>)</mo></math></span> inequality fails.</div></div>\",\"PeriodicalId\":50147,\"journal\":{\"name\":\"Journal of Mathematical Analysis and Applications\",\"volume\":\"544 2\",\"pages\":\"Article 129079\"},\"PeriodicalIF\":1.2000,\"publicationDate\":\"2024-11-22\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Mathematical Analysis and Applications\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0022247X24010011\",\"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 Mathematical Analysis and Applications","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0022247X24010011","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
In this article, we introduce the fractional maximal operator on the Hyperbolic space, a non-doubling measure space, and study its weighted boundedness. Motivated by the weighted boundedness of the Hardy-Littlewood maximal studied by Antezana and Ombrosi in [1], we give conditions for the weak type and strong type estimate for fractional maximal. Also, we present examples of weights for which the fractional maximal operator satisfies weak type inequality but strong type inequality fails.
期刊介绍：
The Journal of Mathematical Analysis and Applications presents papers that treat mathematical analysis and its numerous applications. The journal emphasizes articles devoted to the mathematical treatment of questions arising in physics, chemistry, biology, and engineering, particularly those that stress analytical aspects and novel problems and their solutions.
Papers are sought which employ one or more of the following areas of classical analysis:
• Analytic number theory
• Functional analysis and operator theory
• Real and harmonic analysis
• Complex analysis
• Numerical analysis
• Applied mathematics
• Partial differential equations
• Dynamical systems
• Control and Optimization
• Probability
• Mathematical biology
• Combinatorics
• Mathematical physics.
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