Bernstein inequalities with nondoubling weights

A. Bondarenko; S. Tikhonov

doi:10.4171/JEMS/661

Bernstein inequalities with nondoubling weights

A. Bondarenko, S. Tikhonov

Research output: Contribution to journal › Article › Research › peer-review

3 Citations (Scopus)

Abstract

© 2017 European Mathematical Society. We answer Totik's question on weighted Bernstein inequalities by showing that for all trigonometric polynomials Tn and certain nondoubling weights. Moreover, we find necessary conditions on for Bernstein's inequality to hold. We also prove weighted Markov, Remez, and Nikolskii inequalities for trigonometric and algebraic polynomials.

Original language	English
Pages (from-to)	67-106
Journal	Journal of the European Mathematical Society
Volume	19
Issue number	1
DOIs	https://doi.org/10.4171/JEMS/661
Publication status	Published - 1 Jan 2017

Keywords

Bernstein inequality
Nikolskii inequality
Nondoubling weights
Remez inequality

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10.4171/JEMS/661

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title = "Bernstein inequalities with nondoubling weights",

abstract = "{\textcopyright} 2017 European Mathematical Society. We answer Totik's question on weighted Bernstein inequalities by showing that for all trigonometric polynomials Tn and certain nondoubling weights. Moreover, we find necessary conditions on for Bernstein's inequality to hold. We also prove weighted Markov, Remez, and Nikolskii inequalities for trigonometric and algebraic polynomials.",

keywords = "Bernstein inequality, Nikolskii inequality, Nondoubling weights, Remez inequality",

author = "A. Bondarenko and S. Tikhonov",

year = "2017",

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doi = "10.4171/JEMS/661",

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T1 - Bernstein inequalities with nondoubling weights

AU - Bondarenko, A.

AU - Tikhonov, S.

PY - 2017/1/1

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N2 - © 2017 European Mathematical Society. We answer Totik's question on weighted Bernstein inequalities by showing that for all trigonometric polynomials Tn and certain nondoubling weights. Moreover, we find necessary conditions on for Bernstein's inequality to hold. We also prove weighted Markov, Remez, and Nikolskii inequalities for trigonometric and algebraic polynomials.

AB - © 2017 European Mathematical Society. We answer Totik's question on weighted Bernstein inequalities by showing that for all trigonometric polynomials Tn and certain nondoubling weights. Moreover, we find necessary conditions on for Bernstein's inequality to hold. We also prove weighted Markov, Remez, and Nikolskii inequalities for trigonometric and algebraic polynomials.

KW - Bernstein inequality

KW - Nikolskii inequality

KW - Nondoubling weights

KW - Remez inequality

U2 - 10.4171/JEMS/661

DO - 10.4171/JEMS/661

M3 - Article

SN - 1435-9855

VL - 19

SP - 67

EP - 106

JO - Journal of the European Mathematical Society

JF - Journal of the European Mathematical Society

IS - 1

ER -

Bernstein inequalities with nondoubling weights

Abstract

Keywords

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