A generalization of the Hardy-Littlewood theorem and estimates for the Riesz system in \(\mathbb{R}_+^{n+1}\)
type: Item
instance of: scholarly article
title: A generalization of the Hardy-Littlewood theorem and estimates for the Riesz system in \(\mathbb{R}_+^{n+1}\)
zbMATH Open document ID: 0964.31001
author: M. A. Zakaryan
published in: Journal of Contemporary Mathematical Analysis. Armenian Academy of Sciences
publication date: 2001-07-22T00:00:00Z
review text: Given a harmonic function \(u\) in the unit disk such that \(\int_{-\pi}^\pi|u(re^{i\varphi})|d\varphi\leq \mu(\frac{1}{1-N})\), bounds are found for its harmonic conjugate, provided the function \(\mu\) satisfies certain regularity conditions. Similar results are obtained for harmonic vector fields in a half-space of \(\mathbb{R}^{n+1}\) as well. (There are few misprints in the paper. In particular, the function \(\psi:= \log\varphi\) is not defined in the statement of Theorem 1, and the third assertion of that theorem, however proved, is not formulated).
reviewed by: H.de Arazoza
Mathematics Subject Classification ID: 31A05
Mathematics Subject Classification ID: 31B05
Mathematics Subject Classification ID: 31A20
Mathematics Subject Classification ID: 31B25
zbMATH DE Number: 1532811
zbMATH Keywords: Hardy-Littlewood theorem
zbMATH Keywords: Dzhrbashyan class
zbMATH Keywords: conjugate harmonic function
zbMATH Keywords: harmonic vector field
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1532811