Multivariate polynomial inequalities of different lass="a-plus-plus inline-equation id-i-eq1"> lass="a-plus-plus equation-source format-t-e-x" xmlns:search="http://marklogic.com/appservices/search">\({L_{p,W}(V)}\) -metrics with lass="a-plus-plus">k-concave weights

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• 作者：M. I. Ganzburg
• 关键词：Mathematics Subject Classificationprimary 41A17 ; secondary 26D05
• 刊名：Acta Mathematica Hungarica
• 出版年：2016
• 出版时间：October 2016
• 年：2016
• 卷：150
• 期：1
• 页码：99-120
• 全文大小：886 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Sciences
  Mathematics
  
• 出版者：Akad茅miai Kiad贸, co-published with Springer Science+Business Media B.V., Formerly Kluwer Academic
• ISSN：1588-2632
• 卷排序：150

文摘

Let W be a k-concave weight on an open convex set V in \({{\mathbb R}^m}\), \({k \in [0, \infty]}\), and let \({\mu_W}\) be the weighted measure on V generated by W with \({\mu_W(V) < \infty}\). We find lower and upper estimates of a constant A in the inequality (\({0 \leqq p < q \leqq \infty}\))$$\begin{array}{ll}\bigg(\frac{1}{\mu_W(V)}\int_V \big|P(x)\big|^{q} W(x) \, dx \bigg)^{1/q} \\ \leqq A(n, m, p, q, V, W)\bigg(\frac{1}{\mu_W(V)}\int_V \big|P(x)\big|^p W(x) \, dx\bigg)^{1/p},\end{array}$$where P is a polynomial of m variables of degree at most n. In the case of log-concave measures (k =  0) we improve estimates of A obtained by A. Brudnyi. For \({k \in (0, \infty]}\) estimates of A are new, and we show that they are sharp with respect to n as \({n \to \infty}\). The proofs are based on distributional inequalities for polynomials obtained by Nazarov, Sodin, Volberg, and Fradelizi. 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Timan, Theory of Approximation of Functions of a Real Variable, Pergamon Press (New York, 1963).Copyright information© Akadémiai Kiadó, Budapest, Hungary 2016Authors and AffiliationsM. I. Ganzburg1Email author1.Department of MathematicsHampton UniversityHamptonUSA About this article CrossMark Print ISSN 0236-5294 Online ISSN 1588-2632 Publisher Name Springer Netherlands About this journal Reprints and Permissions Article actions function trackAddToCart() { var buyBoxPixel = new webtrekkV3({ trackDomain: "springergmbh01.webtrekk.net", trackId: "196033507532344", domain: "link.springer.com", contentId: "springer_com.buybox", product: "10.1007/s10474-016-0632-z_Multivariate polynomial inequaliti", productStatus: "add", productCategory : { 1 : "ppv" }, customEcommerceParameter : { 9 : "link.springer.com" } }); buyBoxPixel.sendinfo(); } function trackSubscription() { var subscription = new webtrekkV3({ trackDomain: "springergmbh01.webtrekk.net", trackId: "196033507532344", domain: "link.springer.com", contentId: "springer_com.buybox" }); subscription.sendinfo({linkId: "inst. subscription info"}); } window.addEventListener("load", function(event) { var viewPage = new webtrekkV3({ trackDomain: "springergmbh01.webtrekk.net", trackId: "196033507532344", domain: "link.springer.com", contentId: "SL-article", product: "10.1007/s10474-016-0632-z_Multivariate polynomial inequaliti", productStatus: "view", productCategory : { 1 : "ppv" }, customEcommerceParameter : { 9 : "link.springer.com" } }); viewPage.sendinfo(); }); Log in to check your access to this article Buy (PDF)EUR 34,95 Unlimited access to full article Instant download (PDF) Price includes local sales tax if applicable Find out about institutional subscriptions Export citation .RIS Papers Reference Manager RefWorks Zotero .ENW EndNote .BIB BibTeX JabRef Mendeley Share article Email Facebook Twitter LinkedIn Cookies We use cookies to improve your experience with our site. 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