{"title":"Extension and embedding theorems for Campanato spaces on \n \n \n C\n \n 0\n ,\n γ\n \n \n $C^{0,\\gamma }$\n domains","authors":"Damiano Greco, Pier Domenico Lamberti","doi":"10.1002/mana.202300092","DOIUrl":null,"url":null,"abstract":"<p>We consider Campanato spaces with exponents <span></span><math>\n <semantics>\n <mrow>\n <mi>λ</mi>\n <mo>,</mo>\n <mi>p</mi>\n </mrow>\n <annotation>$\\lambda, p$</annotation>\n </semantics></math> on domains of class <span></span><math>\n <semantics>\n <msup>\n <mi>C</mi>\n <mrow>\n <mn>0</mn>\n <mo>,</mo>\n <mi>γ</mi>\n </mrow>\n </msup>\n <annotation>$C^{0,\\gamma }$</annotation>\n </semantics></math> in the <i>N</i>-dimensional Euclidean space endowed with a natural anisotropic metric depending on <span></span><math>\n <semantics>\n <mi>γ</mi>\n <annotation>$\\gamma$</annotation>\n </semantics></math>. We discuss several results including the appropriate Campanato's embedding theorem and we prove that functions of those spaces can be extended to the whole of the Euclidean space without deterioration of the exponents <span></span><math>\n <semantics>\n <mrow>\n <mi>λ</mi>\n <mo>,</mo>\n <mi>p</mi>\n </mrow>\n <annotation>$\\lambda, p$</annotation>\n </semantics></math>.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"297 6","pages":"2047-2066"},"PeriodicalIF":0.8000,"publicationDate":"2024-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematische Nachrichten","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1002/mana.202300092","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: 0
Abstract
We consider Campanato spaces with exponents on domains of class in the N-dimensional Euclidean space endowed with a natural anisotropic metric depending on . We discuss several results including the appropriate Campanato's embedding theorem and we prove that functions of those spaces can be extended to the whole of the Euclidean space without deterioration of the exponents .
期刊介绍:
Mathematische Nachrichten - Mathematical News publishes original papers on new results and methods that hold prospect for substantial progress in mathematics and its applications. All branches of analysis, algebra, number theory, geometry and topology, flow mechanics and theoretical aspects of stochastics are given special emphasis. Mathematische Nachrichten is indexed/abstracted in Current Contents/Physical, Chemical and Earth Sciences; Mathematical Review; Zentralblatt für Mathematik; Math Database on STN International, INSPEC; Science Citation Index