{"title":"关于Walsh-Kaczmarz系统T均值的极大算子","authors":"N. Gogolashvili, G. Tephnadze","doi":"10.1556/012.2021.58.1.1483","DOIUrl":null,"url":null,"abstract":"In this paper we prove and discuss some new (Hp, Lp,∞) type inequalities of the maximal operators of T means with monotone coefficients with respect to Walsh–Kaczmarz system. It is also proved that these results are the best possible in a special sense. As applications, both some well-known and new results are pointed out. In particular, we apply these results to prove a.e. convergence of such T means.","PeriodicalId":51187,"journal":{"name":"Studia Scientiarum Mathematicarum Hungarica","volume":"45 4 1","pages":""},"PeriodicalIF":0.4000,"publicationDate":"2020-07-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"9","resultStr":"{\"title\":\"On the Maximal Operators of T Means with Respect to Walsh–Kaczmarz System\",\"authors\":\"N. Gogolashvili, G. Tephnadze\",\"doi\":\"10.1556/012.2021.58.1.1483\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper we prove and discuss some new (Hp, Lp,∞) type inequalities of the maximal operators of T means with monotone coefficients with respect to Walsh–Kaczmarz system. It is also proved that these results are the best possible in a special sense. As applications, both some well-known and new results are pointed out. In particular, we apply these results to prove a.e. convergence of such T means.\",\"PeriodicalId\":51187,\"journal\":{\"name\":\"Studia Scientiarum Mathematicarum Hungarica\",\"volume\":\"45 4 1\",\"pages\":\"\"},\"PeriodicalIF\":0.4000,\"publicationDate\":\"2020-07-28\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"9\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Studia Scientiarum Mathematicarum Hungarica\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1556/012.2021.58.1.1483\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Studia Scientiarum Mathematicarum Hungarica","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1556/012.2021.58.1.1483","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
On the Maximal Operators of T Means with Respect to Walsh–Kaczmarz System
In this paper we prove and discuss some new (Hp, Lp,∞) type inequalities of the maximal operators of T means with monotone coefficients with respect to Walsh–Kaczmarz system. It is also proved that these results are the best possible in a special sense. As applications, both some well-known and new results are pointed out. In particular, we apply these results to prove a.e. convergence of such T means.
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The journal publishes original research papers on various fields of mathematics, e.g., algebra, algebraic geometry, analysis, combinatorics, dynamical systems, geometry, mathematical logic, mathematical statistics, number theory, probability theory, set theory, statistical physics and topology.
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