Comparing norms of polynomials in one and several variables
type: Item
instance of: scholarly article
title: Comparing norms of polynomials in one and several variables
zbMATH Open document ID: 0886.30001
author: Igor E. Pritsker
published in: Journal of Mathematical Analysis and Applications
publication date: 1998-05-06T00:00:00Z
review text: The author proves several Nikolskij type inequalities comparing norms of polynomials. If \(P_n\) is a polynomial of degree \(\leq n\), and \(0<p<q \leq\infty\), then \(|P_n |_{L_q (\partial G)} \leq C(p,q)n^k \cdot |P_n|_{L_p (\partial G)}\) where \(k\) depends on \(p,q\) and on the smoothness of the boundary \(\partial G\) of the Jordan domain \(G\). Similarly, area norms \(|P_n |_{L_q (G)}\) and \(|P_n |_{L_p (G)}\) are compared, where \(G\) is assumed to be a quasidisk. These results are extended to polynomials of several complex variables, defined on a product \(H=G_1 \times G_2\times \cdots \times G_m\) of domains.
Mathematics Subject Classification ID: 30C10
Mathematics Subject Classification ID: 41A17
zbMATH DE Number: 1115596
zbMATH Keywords: norms of polynomials
reviewed by: Dieter Gaier
MaRDI profile type: Publication
OpenAlex ID: W1979093993
cites work: Q3752617
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DOI: 10.1006/JMAA.1997.5699
description: scientific article; zbMATH DE number 1115596