{"title":"Sobolev projection on quantum torus, its complete boundedness and applications","authors":"Fedor Sukochev , Kanat Tulenov , Dmitriy Zanin","doi":"10.1016/j.jmaa.2024.128906","DOIUrl":null,"url":null,"abstract":"<div><div>In this paper, we establish the complete boundedness of Sobolev projection from <span><math><msub><mrow><mi>L</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>(</mo><msubsup><mrow><mi>T</mi></mrow><mrow><mi>θ</mi></mrow><mrow><mi>d</mi></mrow></msubsup><mo>)</mo></math></span> into <span><math><msub><mrow><mi>L</mi></mrow><mrow><mn>1</mn><mo>,</mo><mo>∞</mo></mrow></msub><mo>(</mo><msubsup><mrow><mi>T</mi></mrow><mrow><mi>θ</mi></mrow><mrow><mi>d</mi></mrow></msubsup><mo>)</mo></math></span>. In the special case <span><math><mi>θ</mi><mo>=</mo><mn>0</mn></math></span>, our results strengthen the classical results due to Berkson, Bourgain, Pelczynski and Wojciechowski.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"543 2","pages":"Article 128906"},"PeriodicalIF":1.2000,"publicationDate":"2024-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Mathematical Analysis and Applications","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0022247X2400828X","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
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Abstract
In this paper, we establish the complete boundedness of Sobolev projection from into . In the special case , our results strengthen the classical results due to Berkson, Bourgain, Pelczynski and Wojciechowski.
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