{"title":"高斯空间中的 $L_p$$ Blaschke-Santaló 和 Petty 投影不等式","authors":"Junjie Shan, Wenxue Xu, Leiqin Yin","doi":"10.1007/s00013-023-01959-7","DOIUrl":null,"url":null,"abstract":"<div><p>The analogues of the <span>\\(L_p\\)</span> mixed volumes inequality, the <span>\\(L_p\\)</span> Brunn–Minkowski inequality, the <span>\\(L_p\\)</span> Blaschke–Santaló inequality, and the <span>\\(L_p\\)</span> Petty projection inequality in Gaussian space are established.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":null,"pages":null},"PeriodicalIF":0.5000,"publicationDate":"2024-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"\\\\(L_p\\\\) Blaschke–Santaló and Petty projection inequalities in Gaussian space\",\"authors\":\"Junjie Shan, Wenxue Xu, Leiqin Yin\",\"doi\":\"10.1007/s00013-023-01959-7\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>The analogues of the <span>\\\\(L_p\\\\)</span> mixed volumes inequality, the <span>\\\\(L_p\\\\)</span> Brunn–Minkowski inequality, the <span>\\\\(L_p\\\\)</span> Blaschke–Santaló inequality, and the <span>\\\\(L_p\\\\)</span> Petty projection inequality in Gaussian space are established.</p></div>\",\"PeriodicalId\":8346,\"journal\":{\"name\":\"Archiv der Mathematik\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2024-01-12\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Archiv der Mathematik\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s00013-023-01959-7\",\"RegionNum\":4,\"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":"Archiv der Mathematik","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s00013-023-01959-7","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
\(L_p\) Blaschke–Santaló and Petty projection inequalities in Gaussian space
The analogues of the \(L_p\) mixed volumes inequality, the \(L_p\) Brunn–Minkowski inequality, the \(L_p\) Blaschke–Santaló inequality, and the \(L_p\) Petty projection inequality in Gaussian space are established.
期刊介绍：
Archiv der Mathematik (AdM) publishes short high quality research papers in every area of mathematics which are not overly technical in nature and addressed to a broad readership.
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