{"title":"一类多向异性索波列夫空间不同维度的直接和反嵌入定理","authors":"M. A. Khachaturyan","doi":"10.1134/s1055134424020019","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> We consider a class of completely regular polyhedrons <span>\\(\\mathfrak {N} \\)</span> and prove direct and inverse embedding theorems\nfor different dimensions (i.e., theorems on the traces) for functions in the Sobolev multianisotropic\nspace <span>\\( W^{\\mathfrak {N}}_2(\\mathbb {R}^3)\\)</span>.\n</p>","PeriodicalId":39997,"journal":{"name":"Siberian Advances in Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2024-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Direct and Inverse Embedding Theorems for Different Dimensions for a Class of Multianisotropic Sobolev Spaces\",\"authors\":\"M. A. Khachaturyan\",\"doi\":\"10.1134/s1055134424020019\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<h3 data-test=\\\"abstract-sub-heading\\\">Abstract</h3><p> We consider a class of completely regular polyhedrons <span>\\\\(\\\\mathfrak {N} \\\\)</span> and prove direct and inverse embedding theorems\\nfor different dimensions (i.e., theorems on the traces) for functions in the Sobolev multianisotropic\\nspace <span>\\\\( W^{\\\\mathfrak {N}}_2(\\\\mathbb {R}^3)\\\\)</span>.\\n</p>\",\"PeriodicalId\":39997,\"journal\":{\"name\":\"Siberian Advances in Mathematics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-05-31\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Siberian Advances in Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1134/s1055134424020019\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Siberian Advances in Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1134/s1055134424020019","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Direct and Inverse Embedding Theorems for Different Dimensions for a Class of Multianisotropic Sobolev Spaces
Abstract
We consider a class of completely regular polyhedrons \(\mathfrak {N} \) and prove direct and inverse embedding theorems
for different dimensions (i.e., theorems on the traces) for functions in the Sobolev multianisotropic
space \( W^{\mathfrak {N}}_2(\mathbb {R}^3)\).
期刊介绍：
Siberian Advances in Mathematics is a journal that publishes articles on fundamental and applied mathematics. It covers a broad spectrum of subjects: algebra and logic, real and complex analysis, functional analysis, differential equations, mathematical physics, geometry and topology, probability and mathematical statistics, mathematical cybernetics, mathematical economics, mathematical problems of geophysics and tomography, numerical methods, and optimization theory.
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