Some remarks on Turán's inequality. III: The completion
type: Item
instance of: scholarly article
title: Some remarks on Turán's inequality. III: The completion
zbMATH Open document ID: 0849.41005
DOI: 10.1007/BF01909153
published in: Analysis Mathematica
publication date: 1996-10-21T00:00:00Z
review text: [For part II see the author in J. Math. Anal. Appl. 180, No. 1, 138-143 (1993; Zbl 0816.41010).] Let \(H_n\) be the class of real algebraic polynomials of degree \(n\) with all zeros lying in the interval \([- 1,1]\). In a series of research papers the author has examined Turán's inequality. His final version is as follows: Theorem. If \(f \in H_n\), then for \(0 < p \leq v \leq \infty\), \(1 - {1 \over p} + {1 \over q} \geq 0\) \[ |f' |_{L^p} \geq C^* (\sqrt n)^{1 - {1 \over p} + {1 \over q}} |f |_{L^p}. \]
Mathematics Subject Classification ID: 41A17
zbMATH DE Number: 850727
zbMATH Keywords: \(L^ p\)-class
zbMATH Keywords: algebraic polynomials
zbMATH Keywords: Turan's inequality
author: S. P. Zhou
reviewed by: S. M. Mazhar
MaRDI profile type: Publication
cites work: An exact inequality for the derivative of a trigonometric polynomial having only real zeros
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cites work: Q5774835
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cites work: Some remarks on Turán's inequality
cites work: Some remarks on Turán's inequality. II
description: scientific article; zbMATH DE number 850727