On some Nikolskiǐ- and Oswald-type inequalities
type: Item
instance of: scholarly article
title: On some Nikolskiǐ- and Oswald-type inequalities
zbMATH Open document ID: 0655.41020
DOI: 10.1016/0021-9045(87)90013-X
author: Helena Musielak
published in: Journal of Approximation Theory
publication date: 1987-01-01T00:00:00Z
review text: Inequalities are of great value in several contexts. Here the author has developed and discussed in 5 sections through 3 theorems certain properties of inequalities. Estimation of pseudo-norms is one of the main objectives. Inequalities of Nikolskij in \(L^ p_{2\pi}\), \(p\geq 1\), and of Oswald with \(0<p<1\) are extended to the case of Orlicz spaces \(L^{\phi}_{2\pi}\). Two of the theorems can be applied to estimate the averaged moduli of smoothness in \(L^{\phi}_{2\pi}\) by means of best one-sided approximations in terms of trigonometric polynomials.
Mathematics Subject Classification ID: 41A17
zbMATH DE Number: 4069502
zbMATH Keywords: Inequalities
zbMATH Keywords: pseudo-norms
zbMATH Keywords: Orlicz spaces
zbMATH Keywords: trigonometric polynomials
MaRDI profile type: Publication
cites work: Q3743848
cites work: Q3728631
cites work: Orlicz spaces and modular spaces
cites work: Q5816815
cites work: Q4108742
Recommended article: Q3993962
Recommended article: Q3587640
Recommended article: Some Ostrowski type inequalities
Recommended article: On Ostrowski type inequalities
Recommended article: Q5433801
Recommended article: Ul'yanov and Nikol'skii-type inequalities
Recommended article: Q5505239
Recommended article: On Nikol'skii-type inequalities with new characteristics
Recommended article: Some Ostrowski type inequalities and applications
Recommended article: Q5440472
description: scientific article; zbMATH DE number 4069502