Best constant inequalities for conjugate functions
type: Item
instance of: scholarly article
title: Best constant inequalities for conjugate functions
zbMATH Open document ID: 0944.42009
DOI: 10.1016/S0377-0427(99)00015-1
author: Matts Essén
author: Daniel F. Shea
author: Charles S. Stanton
published in: Journal of Computational and Applied Mathematics
publication date: 2000-05-22T00:00:00Z
review text: Let \(F=f+i\widetilde f\) be analytic in the unit disc (in the complex plane) with \(\widetilde f(0)=0\). The authors give a survey on inequalities involving the functions \(F\), \(f\) and \(\widetilde f\) starting with work from the 1920s of M. Riesz and A. Zygmund. The emphasis is on their work during the last 15 years on different kinds of best constant inequalities. In all cases, key points are to construct subharmonic minorants to certain real-valued functions in the complex plane. They explain a general method which will give the old results as well as new inequalities. One of the new results is as follows: There exist absolute constants \(B_0\) and \(B_1\) such that \(\|\widetilde f\|_1\leq 2/\pi\int|f|\log(e+|f|)+B_0\int|f|\log\log(e+|f|)+B_1\|f\|_1\). The first constant \(2/\pi\) is sharp.
Mathematics Subject Classification ID: 42A50
Mathematics Subject Classification ID: 30D55
Mathematics Subject Classification ID: 31A15
zbMATH DE Number: 1334867
zbMATH Keywords: conjugate function
zbMATH Keywords: subharmonic minorant
zbMATH Keywords: best constants
zbMATH Keywords: norm inequalities
reviewed by: Kôzô Yabuta
MaRDI profile type: Publication
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full work available at URL: s0377-0427(99)00015-1
OpenAlex ID: W2015764448
description: scientific article; zbMATH DE number 1334867