{"title":"与球面均值算子有关的伪微分算子的一些结果","authors":"Khaled Hleili, Manel Hleili","doi":"10.1007/s11868-024-00643-w","DOIUrl":null,"url":null,"abstract":"<p>In this paper, we prove a potentially useful <span>\\(L^p(d\\nu )\\)</span>-boundedness result for the pseudo-differential operators associated with the spherical mean operator. Also, boundedness result for symmetrically global pseudo-differential operator on <span>\\(L^p(d\\nu )\\)</span>-type Sobolev space <span>\\(\\mathcal {H}^{u,v,p}\\)</span> of order (<i>u</i>, <i>v</i>) are discussed. An application in solving a generalized heat equation is given.\n</p>","PeriodicalId":48793,"journal":{"name":"Journal of Pseudo-Differential Operators and Applications","volume":"48 1","pages":""},"PeriodicalIF":0.9000,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Some results of pseudo-differential operators related to the spherical mean operator\",\"authors\":\"Khaled Hleili, Manel Hleili\",\"doi\":\"10.1007/s11868-024-00643-w\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>In this paper, we prove a potentially useful <span>\\\\(L^p(d\\\\nu )\\\\)</span>-boundedness result for the pseudo-differential operators associated with the spherical mean operator. Also, boundedness result for symmetrically global pseudo-differential operator on <span>\\\\(L^p(d\\\\nu )\\\\)</span>-type Sobolev space <span>\\\\(\\\\mathcal {H}^{u,v,p}\\\\)</span> of order (<i>u</i>, <i>v</i>) are discussed. An application in solving a generalized heat equation is given.\\n</p>\",\"PeriodicalId\":48793,\"journal\":{\"name\":\"Journal of Pseudo-Differential Operators and Applications\",\"volume\":\"48 1\",\"pages\":\"\"},\"PeriodicalIF\":0.9000,\"publicationDate\":\"2024-09-17\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Pseudo-Differential Operators and Applications\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s11868-024-00643-w\",\"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":"Journal of Pseudo-Differential Operators and Applications","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s11868-024-00643-w","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
Some results of pseudo-differential operators related to the spherical mean operator
In this paper, we prove a potentially useful \(L^p(d\nu )\)-boundedness result for the pseudo-differential operators associated with the spherical mean operator. Also, boundedness result for symmetrically global pseudo-differential operator on \(L^p(d\nu )\)-type Sobolev space \(\mathcal {H}^{u,v,p}\) of order (u, v) are discussed. An application in solving a generalized heat equation is given.
期刊介绍：
The Journal of Pseudo-Differential Operators and Applications is a forum for high quality papers in the mathematics, applications and numerical analysis of pseudo-differential operators. Pseudo-differential operators are understood in a very broad sense embracing but not limited to harmonic analysis, functional analysis, operator theory and algebras, partial differential equations, geometry, mathematical physics and novel applications in engineering, geophysics and medical sciences.
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