Exact order of the Lebesgue constants of hyperbolic partial sums of multiple Fourier series
type: Item
instance of: scholarly article
title: Exact order of the Lebesgue constants of hyperbolic partial sums of multiple Fourier series
zbMATH Open document ID: 0607.42013
DOI: 10.1007/BF01156675
published in: Mathematical Notes
publication date: 1986-01-01T00:00:00Z
review text: The estimates for the speed of growth of the norms of the operators \(H^ N_{\alpha}: f(x)\to \sum_{| m^{\alpha}| \leq N}c_ m(f)e^{im\cdot x}\) as \(N\to \infty\) and the exact order of the quantity \(\sup_{f}\| f-H^ N_{\alpha}\|\) for the classes of functions having bounded mixed derivative are obtained.
Mathematics Subject Classification ID: 42B05
Mathematics Subject Classification ID: 42B99
Mathematics Subject Classification ID: 41A30
zbMATH DE Number: 3981770
zbMATH Keywords: hyperbolic partial sums of continuous periodic functions of several variables
zbMATH Keywords: functions having bounded mixed derivative
author: Elijah Liflyand
reviewed by: W. Łenski
MaRDI profile type: Publication
cites work: Q3284729
cites work: Q4185312
cites work: Discrete imbedding theorems and Lebesgue constants
cites work: Q3913845
full work available at URL: https://doi.org/10.1007/bf01156675
OpenAlex ID: W2048748740
description: scientific article; zbMATH DE number 3981770