Exposed points and external problems in \(H^ 1\). II
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 \(\phi\).
scientific article; zbMATH DE number 3935758