Generalized multiplication operators on weighted Hardy spaces
The authors consider operators \(M^d_\theta f= \theta f'\) for functions \(\theta\) and \(f\) holomorphic in \(\Omega\) and call them ``generalized multiplication'' operators. The paper contains some facts about the action of such operators on what the authors idiosyncratically call ``weighted Hardy spaces'' \(H^p(\beta)\) given by holomorphic functions \(f=\sum_{n}f_n z^n\) with \(\sum_n |f_n|^p\beta_n<\infty\). Then some conditions on the weights for boundedness and compactness are provided. It is also shown that the only case of Hermitian operators occurs whenever \(\theta(z)=az\) for a real number \(a\).
scientific article; zbMATH DE number 6115190