平均n价函数的bernstein型不等式

IF 0.9 3区数学 Q2 MATHEMATICS

Journal of Approximation Theory Pub Date : 2025-05-16 DOI:10.1016/j.jat.2025.106200

Anton Baranov , Ilgiz Kayumov , Rachid Zarouf

引用次数: 0

摘要

给出了单位圆盘中n价平均函数导数的新的积分估计。我们的结果发展和补充了E. P. Dolzhenko和A. A. Pekarskii的估计，以及作者最近得到的不等式。作为应用，我们改进了一些由于Dolzhenko的有理逼近的逆定理。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Bernstein-type inequalities for mean n-valent functions

We derive new integral estimates of the derivatives of mean

n

-valent functions in the unit disc. Our results develop and complement estimates obtained by E. P. Dolzhenko and A. A. Pekarskii, as well as recent inequalities obtained by the authors. As an application, we improve some inverse theorems of rational approximation due to Dolzhenko.

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来源期刊

Journal of Approximation Theory 数学-数学

CiteScore

1.90

自引率

11.10%

发文量

审稿时长

6-12 weeks

期刊介绍： The Journal of Approximation Theory is devoted to advances in pure and applied approximation theory and related areas. These areas include, among others: • Classical approximation • Abstract approximation • Constructive approximation • Degree of approximation • Fourier expansions • Interpolation of operators • General orthogonal systems • Interpolation and quadratures • Multivariate approximation • Orthogonal polynomials • Padé approximation • Rational approximation • Spline functions of one and several variables • Approximation by radial basis functions in Euclidean spaces, on spheres, and on more general manifolds • Special functions with strong connections to classical harmonic analysis, orthogonal polynomial, and approximation theory (as opposed to combinatorics, number theory, representation theory, generating functions, formal theory, and so forth) • Approximation theoretic aspects of real or complex function theory, function theory, difference or differential equations, function spaces, or harmonic analysis • Wavelet Theory and its applications in signal and image processing, and in differential equations with special emphasis on connections between wavelet theory and elements of approximation theory (such as approximation orders, Besov and Sobolev spaces, and so forth) • Gabor (Weyl-Heisenberg) expansions and sampling theory.