On Vladimir Markov type inequality in Lp norms on the interval [-1; 1]-Reference-Cited by-同舟云学术

On Vladimir Markov type inequality in Lp norms on the interval [-1; 1]

Published:2019-12-31 Issue:4 Volume:7 Page:9-12
ISSN:2544-9125
Container-title:Science, Technology and Innovation
language:
Short-container-title:Sci. Tech., Innov

Author:

Baran Mirosław¹,Ozorka Paweł²

Affiliation:

1. Institute of Mathematics, Pedagogical University, Podchorążych 2, 30- 084 Kraków, Poland

2. Department of Mathematics, Faculty of Mathematical and Natural Sciences, University of Applied Sciences in Tarnow, Mickiewicza 8, 33-100 Tarnów, Poland

Abstract

We prove inequality ||P(k)||Lp(-1;1)≤Bp||Tn(k)||Lp(-1;1)n^(2/p) ||P||Lp(-1;1); where Bp are constants independent of n = deg P with 1 ≤ p ≤ 2, which is sharp in the case k ≥ 3. A method presented in this note is based on a factorization of linear operator of k-th derivative throughout normed spaces of polynomial equipped with a Wiener type norm.

Publisher

University of Applied Sciences in Tarnow, Poland

Link

https://stijournal.pl/gicid/pdf/01.3001.0013.7225

Reference21 articles.

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4. M. Baran, A. Kowalska, P. Ozorka, Optimal factors in Vladimir Markov's in-equality in L2 norm, STI (2018).

5. M. Baran, B. Milówka, P. Ozorka, Markov's property for k-th derivative, Ann. Polon. Math., 106 (2012), 31-40.

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