Lipschitz-type and Bloch-type spaces of pluriharmonic mappings in a Hilbert space
The paper considers complex-valued pluriharmonic functions \(f\) on an infinite-dimensional Hilbert space \(E\), i.e., \(f=g+\bar h\) for holomorphic functions \(g\) and \(h\) on a domain in \(E\). First, the functions \(f\) satisfying \(|f(z)-f(w)|\leq C\omega(|z-w|)\) are characterized as those with the similar conditions separately on \(g\) and \(h\), or on \(|g|\) and \(|h|\); here \(\omega\) is a continuous function on \(\mathbb R_+\), \(\omega(0)=0\), such that \(\omega(t)/t\) is increasing. In addition, Bloch-type spaces of pluriharmonic functions on the unit ball of \(E\) are characterized in terms of the ratios \(|f(z)-f(w)|/|z-w|\).
pluriharmonic functions on Hilbert spaces
scientific article; zbMATH DE number 6802011
scientific article