A note on the theorems of Paley and Stein
type: Item
instance of: scholarly article
zbMATH Open document ID: 0973.42023
DOI: 10.1007/BF02515405
author: S. A. Kirillov
publication date: 2001-08-08T00:00:00Z
Mathematics Subject Classification ID: 42C15
Mathematics Subject Classification ID: 46E30
Mathematics Subject Classification ID: 42B35
zbMATH DE Number: 1631379
zbMATH Keywords: Lorentz space
zbMATH Keywords: BMO
zbMATH Keywords: Fourier coefficients
zbMATH Keywords: Lorentz norm
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/bf02515405
OpenAlex ID: W2020189688
title: A note on the theorems of Paley and Stein
published in: Ukraïns'kyĭ Matematychnyĭ Zhurnal
review text: The author gives an estimate of the Lorentz norm of a function in terms of its Fourier coefficients with respect to an orthonormal system \(\{\varphi_n\}\) on \([0,1 ]\), where \(\varphi_n\in\text{BMO}\), and the BMO-seminorm \(\|\varphi_n\|_*\) is bounded. The results generalize the classical theorems by Paley and Stein, and also refine the estimates proposed by \textit{V. I. Kolyada} [Math. Notes, 51, No. 3, 235-244 (1992); translation from Mat. Zametki 51, No. 3, 24-34 (1992; Zbl 0791.42019)].
reviewed by: Anatoly N. Kochubei
description: scientific article; zbMATH DE number 1631379