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

M. Chatzakou, Y. Sarantopoulos
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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.
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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。
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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.
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