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JOURNALS // Matematicheskie Zametki // Archive

Mat. Zametki, 2006 Volume 80, Issue 1, Pages 95–104 (Mi mzm2784)

This article is cited in 2 papers

Inequalities of Bernstein and Jackson–Nikol'skii Type and Estimates of the Norms of Derivatives of Dirichlet Kernels

M. B. Sikhov

Al-Farabi Kazakh National University

Abstract: We obtain Bernstein and Jackson–Nikol'skii inequalities for trigonometric polynomials with spectrum generated by the level surfaces of a function $\Lambda(t)$, and their sharpness is studied under a specific choice of $\Lambda(t)$. Estimates of the norms of derivatives of Dirichlet kernels with harmonics generated by the level surfaces of the function $\Lambda(t)$ are established in $L^p$.

Keywords: Bernstein-type inequality, Jackson–Nikol'skii inequality, Dirichlet kernel, trigonometric polynomial, spectrum of a polynomial, hyperbolic cross.

UDC: 517.518.8

Received: 20.07.2004
Revised: 12.09.2005

DOI: 10.4213/mzm2784


 English version:
Mathematical Notes, 2006, 80:1, 91–100

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