Bernstein and Markov-type inequalities for polynomials on Lp(μ) spaces

M. Chatzakou, Y. Sarantopoulos
{"title":"Bernstein and Markov-type inequalities for polynomials on Lp(μ) spaces","authors":"M. Chatzakou, Y. Sarantopoulos","doi":"10.14658/pupj-drna-2019-Special_Issue-4","DOIUrl":null,"url":null,"abstract":"In this work, we discuss generalizations of the classical Bernstein and Markov type inequalities for polynomials and we present some new inequalities for the $k$th Frechet derivative of homogeneous polynomials on real and complex $L_{p}(\\mu)$ spaces. We also give applications to homogeneous polynomials and symmetric multilinear mappings in $L_{p}(\\mu)$ spaces. Finally, Bernstein's inequality for homogeneous polynomials on both real and complex Hilbert spaces has been discussed.","PeriodicalId":51943,"journal":{"name":"Dolomites Research Notes on Approximation","volume":null,"pages":null},"PeriodicalIF":0.6000,"publicationDate":"2020-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Dolomites Research Notes on Approximation","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.14658/pupj-drna-2019-Special_Issue-4","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 3

Abstract

In this work, we discuss generalizations of the classical Bernstein and Markov type inequalities for polynomials and we present some new inequalities for the $k$th Frechet derivative of homogeneous polynomials on real and complex $L_{p}(\mu)$ spaces. We also give applications to homogeneous polynomials and symmetric multilinear mappings in $L_{p}(\mu)$ spaces. Finally, Bernstein's inequality for homogeneous polynomials on both real and complex Hilbert spaces has been discussed.
查看原文
分享 分享
微信好友 朋友圈 QQ好友 复制链接
本刊更多论文
Lp(μ)空间上多项式的Bernstein和Markov型不等式
在这项工作中,我们讨论了多项式的经典Bernstein和Markov型不等式的推广,并给出了实和复$L_{p}(\mu)$空间上齐次多项式的$k$th Frechet导数的一些新不等式。我们还给出了$L_{p}(\mu)$空间中齐次多项式和对称多线性映射的应用。最后,讨论了实Hilbert空间和复Hilbert空间上齐次多项式的Bernstein不等式。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 去求助
来源期刊
CiteScore
1.70
自引率
7.70%
发文量
0
审稿时长
8 weeks
期刊介绍: Dolomites Research Notes on Approximation is an open access journal that publishes peer-reviewed papers. It also publishes lecture notes and slides of the tutorials presented at the annual Dolomites Research Weeks and Workshops, which have been organized regularly since 2006 by the Padova-Verona Research Group on Constructive Approximation and Applications (CAA) in Alba di Canazei (Trento, Italy). The journal publishes, on invitation, survey papers and summaries of Ph.D. theses on approximation theory, algorithms, and applications.
期刊最新文献
Positivity-preserving and elementary stable nonstandard method for a COVID-19 SIR model Computation of the Bell-Laplace transforms Bernstein and Markov-type inequalities for polynomials on Lp(μ) spaces RBF-based tensor decomposition with applications to oenology Hopf bifurcation analysis of the fast subsystem of a polynomial phantom burster model
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
0
微信
客服QQ
Book学术公众号 扫码关注我们
反馈
×
意见反馈
请填写您的意见或建议
请填写您的手机或邮箱
已复制链接
已复制链接
快去分享给好友吧!
我知道了
×
扫码分享
扫码分享
Book学术官方微信
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术
文献互助 智能选刊 最新文献 互助须知 联系我们:info@booksci.cn
Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。
Copyright © 2023 Book学术 All rights reserved.
ghs 京公网安备 11010802042870号 京ICP备2023020795号-1