A pointwise cubic average for two commuting transformations
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- 作者：Sebastián Donoso ; Wenbo Sun
- 刊名：Israel Journal of Mathematics
- 出版年：2016
- 出版时间：October 2016
- 年：2016
- 卷：216
- 期：2
- 页码：657-678
- 全文大小：277 KB
- 刊物类别：Mathematics and Statistics
- 刊物主题：Mathematics
Mathematics
Algebra
Group Theory and Generalizations
Analysis
Applications of Mathematics
Mathematical and Computational Physics - 出版者：Hebrew University Magnes Press
- ISSN：1565-8511
- 卷排序：216
文摘
Huang, Shao and Ye recently studied pointwise multiple averages by using suitable topological models. Using a notion of dynamical cubes introduced by the authors, the Huang–Shao–Ye technique and the Host machinery of magic systems, we prove that for a system (X, µ, S, T) with commuting transformations S and T, the average $$\frac{1}{{{N^2}}}\sum\limits_{i,j = 0}^{N - 1} {{f_0}} \left( {{S^i}x} \right){f_1}\left( {{T^j}x} \right){f_2}\left( {{S^i}{T^j}x} \right)$$ converges a.e. as N goes to infinity for any f0, f1, f2 ∈ L∞(µ).References[1]I. Assani, Pointwise convergence of ergodic averages along cubes, J. Analyse Math. 110 (2010), 241–269.MathSciNetCrossRefMATHGoogle Scholar[2]T. Austin, On the norm convergence of nonconventional ergodic averages, Ergodic Theory and Dynamical Systems 30 (2010), 321–338.MathSciNetCrossRefMATHGoogle Scholar[3]V. Bergelson, The multifarious Poincaré Recurrence Theorem, in Descriptive Set Theory and Dynamical Systems, (M. Foreman, A. S. Kechris, A. 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(N.S.) 13 (1985), 143–146.MathSciNetCrossRefMATHGoogle ScholarCopyright information© Hebrew University of Jerusalem 2016Authors and AffiliationsSebastián Donoso12Email authorWenbo Sun31.Centro de Modelamiento Matemático and Departamento de Ingeniería MatemáticaUniversidad de ChileSantiagoChile2.Université Paris-EstLaboratoire d’analyse et de mathématiques appliquéesMarne la Vallée Cedex 2France3.Department of MathematicsNorthwestern UniversityEvanstonUSA About this article CrossMark Print ISSN 0021-2172 Online ISSN 1565-8511 Publisher Name The Hebrew University Magnes Press 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/s11856-016-1423-5_A pointwise cubic average for two ", 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/s11856-016-1423-5_A pointwise cubic average for two ", 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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