Approximation of periodic functions by Zygmund means
type: Item
instance of: scholarly article
title: Approximation of periodic functions by Zygmund means
zbMATH Open document ID: 0637.42004
DOI: 10.1007/BF01170248
author: N. A. Il'yasov
published in: Mathematical Notes
publication date: 1986-01-01T00:00:00Z
review text: Let \(E_ p(\epsilon)=\{f\in L_ p:\) \(E_ n(f)_ p\leq \epsilon_ n\), \(n\in Z_+\}\) where \(\epsilon =\{\epsilon_ n\}\) with \(0<\epsilon_ n\downarrow 0\), and let \(H^{\ell}_ p[\omega]\{f\in L_ p:\omega_{\ell}(f,\delta)\leq \omega (\delta)\) \((\delta \downarrow +0)\}\); \(L_ p\), \(1\leq p<\infty\) the space of all measurable \(2\pi\)- periodic functions for which \(\| f\|_ p=(1/\pi \int^{2\pi}_{0}| f(x)|^ p dx)^{1/p}<\infty\), \(L_{\infty}=C\) the space of continuous functions. The author solves the problem for exact order of approximation with normal Zygmund means for the function classes \(E_ p(\epsilon)\) and \(H^{\ell}_ p[\omega]\), \(1\leq p\leq \infty\).
Mathematics Subject Classification ID: 42A24
zbMATH DE Number: 4038441
zbMATH Keywords: Zygmund means
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4038441