{"title":"L 2 a (ℝ+;ma(x)dx) 中涉及索引惠特克变换的一对伪微分算子","authors":"Jeetendrasingh Maan, Akhilesh Prasad","doi":"10.1007/s10114-024-3162-6","DOIUrl":null,"url":null,"abstract":"<div><p>Pseudo-differential operators (PDO) <span>\\(Q(x,{{\\cal L}_{a,x}})\\)</span> and <span>\\({\\cal Q}(x,{{\\cal L}_{a,x}})\\)</span> involving the index Whittaker transform are defined. Estimates for these operators in Hilbert space <i>L</i><span>\n <sup><i>a</i></sup><sub>2</sub>\n \n </span>(ℝ<sub>+</sub>;<i>m</i><sub><i>a</i></sub>(<i>x</i>)<i>dx</i>) are obtained. A symbol class Ω is introduced. Later product and commutators for the PDO are investigated and their boundedness results are discussed.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"40 6","pages":"1420 - 1430"},"PeriodicalIF":0.8000,"publicationDate":"2024-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A Pair of Pseudo-differential Operators Involving Index Whittaker Transform in L\\n a2\\n \\n (ℝ+;ma(x)dx)\",\"authors\":\"Jeetendrasingh Maan, Akhilesh Prasad\",\"doi\":\"10.1007/s10114-024-3162-6\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>Pseudo-differential operators (PDO) <span>\\\\(Q(x,{{\\\\cal L}_{a,x}})\\\\)</span> and <span>\\\\({\\\\cal Q}(x,{{\\\\cal L}_{a,x}})\\\\)</span> involving the index Whittaker transform are defined. Estimates for these operators in Hilbert space <i>L</i><span>\\n <sup><i>a</i></sup><sub>2</sub>\\n \\n </span>(ℝ<sub>+</sub>;<i>m</i><sub><i>a</i></sub>(<i>x</i>)<i>dx</i>) are obtained. A symbol class Ω is introduced. Later product and commutators for the PDO are investigated and their boundedness results are discussed.</p></div>\",\"PeriodicalId\":50893,\"journal\":{\"name\":\"Acta Mathematica Sinica-English Series\",\"volume\":\"40 6\",\"pages\":\"1420 - 1430\"},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2024-04-15\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Acta Mathematica Sinica-English Series\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s10114-024-3162-6\",\"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":"Acta Mathematica Sinica-English Series","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s10114-024-3162-6","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
A Pair of Pseudo-differential Operators Involving Index Whittaker Transform in L
a2
(ℝ+;ma(x)dx)
Pseudo-differential operators (PDO) \(Q(x,{{\cal L}_{a,x}})\) and \({\cal Q}(x,{{\cal L}_{a,x}})\) involving the index Whittaker transform are defined. Estimates for these operators in Hilbert space La2(ℝ+;ma(x)dx) are obtained. A symbol class Ω is introduced. Later product and commutators for the PDO are investigated and their boundedness results are discussed.
期刊介绍：
Acta Mathematica Sinica, established by the Chinese Mathematical Society in 1936, is the first and the best mathematical journal in China. In 1985, Acta Mathematica Sinica is divided into English Series and Chinese Series. The English Series is a monthly journal, publishing significant research papers from all branches of pure and applied mathematics. It provides authoritative reviews of current developments in mathematical research. Contributions are invited from researchers from all over the world.
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