Some generalizations of contraction theorems for Fourier series
type: Item
instance of: scholarly article
title: Some generalizations of contraction theorems for Fourier series
zbMATH Open document ID: 0533.42006
author: Masakiti Kinukawa
published in: Pacific Journal of Mathematics
publication date: 1983-01-01T00:00:00Z
review text: Let \(f\in L_{2\pi}\), \(f\sim \sum^{\infty}_{n=-\infty}c_ ne^{inx}\), \(0<p\leq 2\), and let I(t) be a positive, increasing function in (0,1) satisfying some inequalities. After generalizing B. S. Yadov's theorem on absolute convergence with power p of the series of Fourier coefficients of the shrivel contraction of f, there are given by means of the sequence \(\{c_ n\}\) necessary and sufficient conditions in order that \(A_{p,j,I}(f)=\{\int^{1}_{0}[\int^{2\pi}_{0}| \Delta^ j\!_ tf(x)I^{-1}(t)|^ 2dx]^{p/2}\frac{dt}{t}\}^{1/p}<\infty.\) where \(\Delta^ j\!_ tf(x)\) is the ordinary difference of f of order j.
Mathematics Subject Classification ID: 42A20
zbMATH DE Number: 3846169
zbMATH Keywords: shrivel contraction
zbMATH Keywords: Lipschitz spaces
zbMATH Keywords: symmetric difference
reviewed by: Julian Musielak
MaRDI profile type: Publication
full work available at URL: pjm.1983.109.121
OpenAlex ID: W2069636193
DOI: 10.2140/PJM.1983.109.121
Recommended article: Q4712997
Recommended article: Q3712761
Recommended article: Q4712600
Recommended article: On the generalized absolute convergence of Fourier series
Recommended article: A generalization of Lebesgue's convergence criterion for Fourier series
Recommended article: On a generalization of Fourier series
Recommended article: Convergence and Summability of Multiple Fourier series and generalized variation
Recommended article: Convergence of generalized conjugate partial sums of Fourier series
Recommended article: Some problems of convergence of general Fourier series
description: scientific article; zbMATH DE number 3846169