This paper is devoted to characterizing the analytic Campanato spaces AL p,η (including the analytic Morrey spaces, the analytic John-Nirenberg space, and the analytic Lipschitz/Hölder spaces) on the complex unit disk D in terms of the Möbius mappings and the Littlewood-Paley forms, and consequently their compositions with the analytic self-maps of D.

No abstract

The analytic spaceF(p,q,s)can be embedded into a Bloch-type space. We establish a distance formula from Bloch-type functions toF(p,q,s), which generalizes the distance formula from Bloch functions to BMOA by Peter Jones, and toF(p,p-2,s)by Zhao.

Using Carleson measure theorem of weighted Bergman spaces, we provide a complete characterization of embedding theorem for Dirichlet type spaces. As an application, we study the Volterra integral operator and multipliers for Dirichlet type spaces.2000 Mathematics Subject Classification. 30H30, 47B38.

No abstract