Analytic Campanato spaces by functionals and operators (Q345304)

The paper is a nice study of the analytic Campanato space \(\mathcal{CA}_p\) on the unit disk \(\mathbb D\) of the complex plane \(\mathbb C\). After an introduction into the topic, the study has two main sections concerning with the behaviour of functionals and operators on Campanato spaces. In the section devoted to the functionals, Choquet integration and quadratic Tent space are analyzed, then the first predual and the second predual of \(\mathcal{CA}_p\) are explored. In the section devoted to operators on Campanato spaces, the case when the superposition operator is bounded, the boundedness of the backward shift operator, and the behaviour of the Schwarzian derivative of a univalent analytic function on \(\mathbb D\), whenever \(\log f'\) belongs to a Campanato space, are investigated.