{"title":"可变各向异性分数积分算子","authors":"B. D. Li, J. W. Sun, Z. Z. Yang","doi":"10.1007/s10474-023-01368-w","DOIUrl":null,"url":null,"abstract":"<div><p>In 2011, Dekel et al. introduced a highly geometric Hardy spaces <span>\\(H^p(\\Theta)\\)</span>, for the full range <span>\\(0<p\\le 1\\)</span>, which are constructed over a continuous multilevel\nellipsoid cover <span>\\(\\Theta\\)</span> of <span>\\(\\mathbb{R}^n\\)</span> with high anisotropy in the sense that the ellipsoids\ncan change shape rapidly from point to point and from level to level. We introduce\na new class of fractional integral operators <span>\\(T_{\\alpha}\\)</span> adapted to ellipsoid cover <span>\\(\\Theta\\)</span> and\nobtained their boundedness from <span>\\(H^p(\\Theta)\\)</span> to <span>\\(H^q(\\Theta)\\)</span> and from <span>\\(H^p(\\Theta)\\)</span> to <span>\\(L^q(\\mathbb{R}^n)\\)</span>,\nwhere <span>\\(\\frac{1}{q}=\\frac{1}{p}+\\alpha\\)</span> and <span>\\(0<\\alpha<1\\)</span>.</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":null,"pages":null},"PeriodicalIF":0.6000,"publicationDate":"2023-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10474-023-01368-w.pdf","citationCount":"0","resultStr":"{\"title\":\"Variable anisotropic fractional integral operators\",\"authors\":\"B. D. Li, J. W. Sun, Z. Z. Yang\",\"doi\":\"10.1007/s10474-023-01368-w\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>In 2011, Dekel et al. introduced a highly geometric Hardy spaces <span>\\\\(H^p(\\\\Theta)\\\\)</span>, for the full range <span>\\\\(0<p\\\\le 1\\\\)</span>, which are constructed over a continuous multilevel\\nellipsoid cover <span>\\\\(\\\\Theta\\\\)</span> of <span>\\\\(\\\\mathbb{R}^n\\\\)</span> with high anisotropy in the sense that the ellipsoids\\ncan change shape rapidly from point to point and from level to level. We introduce\\na new class of fractional integral operators <span>\\\\(T_{\\\\alpha}\\\\)</span> adapted to ellipsoid cover <span>\\\\(\\\\Theta\\\\)</span> and\\nobtained their boundedness from <span>\\\\(H^p(\\\\Theta)\\\\)</span> to <span>\\\\(H^q(\\\\Theta)\\\\)</span> and from <span>\\\\(H^p(\\\\Theta)\\\\)</span> to <span>\\\\(L^q(\\\\mathbb{R}^n)\\\\)</span>,\\nwhere <span>\\\\(\\\\frac{1}{q}=\\\\frac{1}{p}+\\\\alpha\\\\)</span> and <span>\\\\(0<\\\\alpha<1\\\\)</span>.</p></div>\",\"PeriodicalId\":50894,\"journal\":{\"name\":\"Acta Mathematica Hungarica\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2023-09-04\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://link.springer.com/content/pdf/10.1007/s10474-023-01368-w.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Acta Mathematica Hungarica\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s10474-023-01368-w\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Acta Mathematica Hungarica","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s10474-023-01368-w","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
Variable anisotropic fractional integral operators
In 2011, Dekel et al. introduced a highly geometric Hardy spaces \(H^p(\Theta)\), for the full range \(0<p\le 1\), which are constructed over a continuous multilevel
ellipsoid cover \(\Theta\) of \(\mathbb{R}^n\) with high anisotropy in the sense that the ellipsoids
can change shape rapidly from point to point and from level to level. We introduce
a new class of fractional integral operators \(T_{\alpha}\) adapted to ellipsoid cover \(\Theta\) and
obtained their boundedness from \(H^p(\Theta)\) to \(H^q(\Theta)\) and from \(H^p(\Theta)\) to \(L^q(\mathbb{R}^n)\),
where \(\frac{1}{q}=\frac{1}{p}+\alpha\) and \(0<\alpha<1\).
期刊介绍:
Acta Mathematica Hungarica is devoted to publishing research articles of top quality in all areas of pure and applied mathematics as well as in theoretical computer science. The journal is published yearly in three volumes (two issues per volume, in total 6 issues) in both print and electronic formats. Acta Mathematica Hungarica (formerly Acta Mathematica Academiae Scientiarum Hungaricae) was founded in 1950 by the Hungarian Academy of Sciences.