Analogs of the Jackson-Nikol'skij inequalities for trigonometric polynomials in spaces with nonsymmetric norm
type: Item
instance of: scholarly article
title: Analogs of the Jackson-Nikol'skij inequalities for trigonometric polynomials in spaces with nonsymmetric norm
zbMATH Open document ID: 0915.42001
DOI: 10.1007/BF02355078
author: A. I. Kozko
published in: Mathematical Notes
publication date: 1999-07-05T00:00:00Z
review text: The author deals with the evaluation of \[ \sup_{\substack{ t_n\in T_n\\ t_n\not\equiv 0}} {\| t_n\|_{q_1,q_2}\over\| t_n\|_{p_1,p_2}}, \] where \(\| f\|_{p,q}:= \| f^+\|_p+\| f^-\|_q\) denotes the nonsymmetric norm of \(f\). E.g., he proves that if \(1\leq p\leq\infty\), then \[ \sup_{\substack{ t_n\in T_n\\ t_n\not\equiv 0}} {\| t_n\|_{1,\infty}\over \| t_n\|_{1,p}}\asymp n^{3/(2p+ 1)}. \] {}.
Mathematics Subject Classification ID: 42A05
Mathematics Subject Classification ID: 41A17
zbMATH DE Number: 1238045
zbMATH Keywords: trigonometric polynomials
zbMATH Keywords: Jackson-Nikol'skij inequality
reviewed by: László Leindler
MaRDI profile type: Publication
cites work: Certain problems of closest approximation
cites work: Q3937799
cites work: Q5337337
description: scientific article; zbMATH DE number 1238045