{"title":"$L^p$-boundedness of pseudo-differential operators on homogeneous trees","authors":"Tapendu Rana, Sumit Kumar Rano","doi":"10.4064/sm220816-27-3","DOIUrl":null,"url":null,"abstract":". The aim of this article is to study the L p -boundedness of pseudo-differen-tial operators on a homogeneous tree X . For p ∈ (1 , 2) , we establish a connection between the L p -boundedness of the pseudo-differential operators on X and that on the group of integers Z . We also prove an analogue of the Calderón–Vaillancourt theorem in the setting of homogeneous trees for p ∈ (1 , ∞ ) \\ { 2 } .","PeriodicalId":51179,"journal":{"name":"Studia Mathematica","volume":"1 1","pages":""},"PeriodicalIF":0.7000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Studia Mathematica","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4064/sm220816-27-3","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 1
Abstract
. The aim of this article is to study the L p -boundedness of pseudo-differen-tial operators on a homogeneous tree X . For p ∈ (1 , 2) , we establish a connection between the L p -boundedness of the pseudo-differential operators on X and that on the group of integers Z . We also prove an analogue of the Calderón–Vaillancourt theorem in the setting of homogeneous trees for p ∈ (1 , ∞ ) \ { 2 } .
期刊介绍:
The journal publishes original papers in English, French, German and Russian, mainly in functional analysis, abstract methods of mathematical analysis and probability theory.