{"title":"鞅Hardy Orlicz-Lorentz-Karamata空间及其在傅里叶分析中的应用","authors":"Z. Hao, F. Weisz","doi":"10.1007/s10476-024-00057-2","DOIUrl":null,"url":null,"abstract":"<div><p> We summarize some results as well as we prove some new results about the Orlicz–Lorentz–Karamata spaces and martingale Hardy Orlicz–Lorentz–Karamata spaces. More precisely, Doob's maximal inequality for submartingales and Burkholder–Davis–Gundy inequality are presented. We also show some fundamental martingale inequalities and modular inequalities. Additionally, based on atomic decompositions, duality theorems and fractional integral operators are discussed. As applications in Fourier analysis, we consider the Walsh–Fourier series on Orlicz–Lorentz–Karamata spaces. The dyadic maximal operators on martingale Hardy Orlicz–Lorentz–Karamata spaces are presented. The boundedness of maximal Fejér operator is proved, which further implies some convergence results of the Fejér means.\n</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":"50 4","pages":"1045 - 1071"},"PeriodicalIF":0.6000,"publicationDate":"2024-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10476-024-00057-2.pdf","citationCount":"0","resultStr":"{\"title\":\"Martingale Hardy Orlicz–Lorentz–Karamata spaces and applications in Fourier analysis\",\"authors\":\"Z. Hao, F. Weisz\",\"doi\":\"10.1007/s10476-024-00057-2\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p> We summarize some results as well as we prove some new results about the Orlicz–Lorentz–Karamata spaces and martingale Hardy Orlicz–Lorentz–Karamata spaces. More precisely, Doob's maximal inequality for submartingales and Burkholder–Davis–Gundy inequality are presented. We also show some fundamental martingale inequalities and modular inequalities. Additionally, based on atomic decompositions, duality theorems and fractional integral operators are discussed. As applications in Fourier analysis, we consider the Walsh–Fourier series on Orlicz–Lorentz–Karamata spaces. The dyadic maximal operators on martingale Hardy Orlicz–Lorentz–Karamata spaces are presented. The boundedness of maximal Fejér operator is proved, which further implies some convergence results of the Fejér means.\\n</p></div>\",\"PeriodicalId\":55518,\"journal\":{\"name\":\"Analysis Mathematica\",\"volume\":\"50 4\",\"pages\":\"1045 - 1071\"},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2024-11-04\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://link.springer.com/content/pdf/10.1007/s10476-024-00057-2.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Analysis Mathematica\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s10476-024-00057-2\",\"RegionNum\":3,\"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":"Analysis Mathematica","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s10476-024-00057-2","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
Martingale Hardy Orlicz–Lorentz–Karamata spaces and applications in Fourier analysis
We summarize some results as well as we prove some new results about the Orlicz–Lorentz–Karamata spaces and martingale Hardy Orlicz–Lorentz–Karamata spaces. More precisely, Doob's maximal inequality for submartingales and Burkholder–Davis–Gundy inequality are presented. We also show some fundamental martingale inequalities and modular inequalities. Additionally, based on atomic decompositions, duality theorems and fractional integral operators are discussed. As applications in Fourier analysis, we consider the Walsh–Fourier series on Orlicz–Lorentz–Karamata spaces. The dyadic maximal operators on martingale Hardy Orlicz–Lorentz–Karamata spaces are presented. The boundedness of maximal Fejér operator is proved, which further implies some convergence results of the Fejér means.
期刊介绍：
Traditionally the emphasis of Analysis Mathematica is classical analysis, including real functions (MSC 2010: 26xx), measure and integration (28xx), functions of a complex variable (30xx), special functions (33xx), sequences, series, summability (40xx), approximations and expansions (41xx).
The scope also includes potential theory (31xx), several complex variables and analytic spaces (32xx), harmonic analysis on Euclidean spaces (42xx), abstract harmonic analysis (43xx).
The journal willingly considers papers in difference and functional equations (39xx), functional analysis (46xx), operator theory (47xx), analysis on topological groups and metric spaces, matrix analysis, discrete versions of topics in analysis, convex and geometric analysis and the interplay between geometry and analysis.
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