Exposed points and external problems in \(H^ 1\). II
type: Item
instance of: scholarly article
title: Exposed points and external problems in \(H^ 1\). II
zbMATH Open document ID: 0584.46041
author: Takahiko Nakazi
published in: Tôhoku Mathematical Journal. Second Series
publication date: 1984-01-01T00:00:00Z
review text: If \(\phi\in L^{\infty}\), we denote by \(T_{\phi}\) the functional defined on the Hardy space \(H^ 1\) by \(T_{\phi}(f)=\int^{\pi}_{- \pi}f(e^{i\theta})\phi(e^{i\theta})d\theta /2\pi\). let \(S_{\phi}\) be the set of functions in \(H^ 1\) which satisfy \(T_{\phi}(f)=\| T_{\phi}\|\) and \(\| f\|_ 1\leq 1\). If \(S_{\phi}\) is not empty and weak-*compact, a description of \(S_{\phi}\) was given in the first part of this paper [J. Funct. Anal. 53, 224-230 (1983; Zbl 0527.46049)]. In this paper, the structure of \(S_{\phi}\) is studied generally. Moreover, we give a characterization of exposed points, that is, g in \(H^ 1\) such that \(S_{\phi}=\{g\}\) for some \(\phi\).
Mathematics Subject Classification ID: 46J15
Mathematics Subject Classification ID: 30D55
Mathematics Subject Classification ID: 30D50
zbMATH DE Number: 3935758
zbMATH Keywords: extremal problems
zbMATH Keywords: exposed points
zbMATH Keywords: strong outer functions
zbMATH Keywords: Hardy space
zbMATH Keywords: weak-*compact
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2748/tmj/1178228683
OpenAlex ID: W2108159275
cites work: Extreme points and extremum problems in \(H_1\)
cites work: Q3874458
cites work: Exposed points and extremal problems in \(H_ 1\)
cites work: Some uniqueness theorems for \(H^p(U^n)\) functions
DOI: 10.2748/TMJ/1178228683
description: scientific article; zbMATH DE number 3935758