{"title":"Heisenberg群上分数阶Sobolev空间上的Hardy型不等式","authors":"A. Adimurthi, Arka Mallick","doi":"10.2422/2036-2145.201604_010","DOIUrl":null,"url":null,"abstract":"In this paper, we derive a non linear Hardy type inequality on certain \nfractional order Sobolev spaces on the Heisenberg group. Our inequality is an \nanalogous version of an inequality of the same name on weighted Folland-Stein \nspaces which had been derived in [3]. We also derive Sobolev type and Morrey \ntype embedding to make that abstract fractional order Sobolev spaces on the \nHeisenberg group more familiar.","PeriodicalId":50966,"journal":{"name":"Annali Della Scuola Normale Superiore Di Pisa-Classe Di Scienze","volume":"63 1","pages":"917-949"},"PeriodicalIF":1.2000,"publicationDate":"2018-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"19","resultStr":"{\"title\":\"A Hardy type inequality on fractional order Sobolev spaces on the Heisenberg group\",\"authors\":\"A. Adimurthi, Arka Mallick\",\"doi\":\"10.2422/2036-2145.201604_010\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we derive a non linear Hardy type inequality on certain \\nfractional order Sobolev spaces on the Heisenberg group. Our inequality is an \\nanalogous version of an inequality of the same name on weighted Folland-Stein \\nspaces which had been derived in [3]. We also derive Sobolev type and Morrey \\ntype embedding to make that abstract fractional order Sobolev spaces on the \\nHeisenberg group more familiar.\",\"PeriodicalId\":50966,\"journal\":{\"name\":\"Annali Della Scuola Normale Superiore Di Pisa-Classe Di Scienze\",\"volume\":\"63 1\",\"pages\":\"917-949\"},\"PeriodicalIF\":1.2000,\"publicationDate\":\"2018-05-21\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"19\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Annali Della Scuola Normale Superiore Di Pisa-Classe Di Scienze\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.2422/2036-2145.201604_010\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annali Della Scuola Normale Superiore Di Pisa-Classe Di Scienze","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.2422/2036-2145.201604_010","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
A Hardy type inequality on fractional order Sobolev spaces on the Heisenberg group
In this paper, we derive a non linear Hardy type inequality on certain
fractional order Sobolev spaces on the Heisenberg group. Our inequality is an
analogous version of an inequality of the same name on weighted Folland-Stein
spaces which had been derived in [3]. We also derive Sobolev type and Morrey
type embedding to make that abstract fractional order Sobolev spaces on the
Heisenberg group more familiar.
期刊介绍：
The Annals of the Normale Superiore di Pisa, Science Class, publishes papers that contribute to the development of Mathematics both from the theoretical and the applied point of view. Research papers or papers of expository type are considered for publication.
The Annals of the Normale Scuola di Pisa - Science Class is published quarterly
Soft cover, 17x24
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