The space BMO and strong means of Fourier series
type: Item
instance of: scholarly article
title: The space BMO and strong means of Fourier series
zbMATH Open document ID: 0731.42013
DOI: 10.1007/BF02630362
author: V. A. Rodin
published in: Analysis Mathematica
publication date: 1990-01-01T00:00:00Z
review text: Let \(S_ k(f,x)\) be the partial sum of the Fourier (trigonometric) series of the function f and \(\tilde S_ k(f,x)\) the partial sum of the conjugate series. Let \(\Delta^ n_ k[k/n,(k+1)/n)\quad (k=0,1,...,n- 1)\) and define \(\kappa_{\Delta^ n_ k}(t)=1\) if \(t\in \Delta^ n_ k\) and \(\kappa_{\Delta^ n_ k}(t)=0\) if \(t\in [0,1)\setminus \Delta^ n_ k.\) The author proves that the operator \[ (Bf)(x)=\sup_{0\leq n<\infty}\| \sum^{2^ n-1}_{k=0}S_ k(f,x)\kappa_{\Delta_ k^{2^ n}}(t)\|_{BMO[0,1)} \] is of weak ype (1,1) and similarly for the operator corresponding to \(\tilde S_ k(f,x)\).
reviewed by: S.Aljančić
Mathematics Subject Classification ID: 42A50
Mathematics Subject Classification ID: 42A20
Mathematics Subject Classification ID: 42A24
zbMATH DE Number: 4208770
zbMATH Keywords: strong means of Fourier series
zbMATH Keywords: sublinear operators
zbMATH Keywords: Banach space BMO
zbMATH Keywords: conjugate series
MaRDI profile type: Publication
cites work: Period, index and potential \(\text Ш\)
cites work: Q3506242
cites work: Rademacher series in symmetric spaces
cites work: On limits of sequences of operators
description: scientific article; zbMATH DE number 4208770