Two Predualities and Three Operators over Analytic Campanato Spaces

TL;DR

This paper characterizes the preduals of analytic Campanato spaces and studies the boundedness of superposition, backward shift, and Schwarzian derivative operators on these spaces.

Contribution

It provides a complete description of the predual spaces of $\\mathcal{CA}_p$ and analyzes the boundedness of three important operators on these spaces.

Findings

Characterization of the first and second preduals of $\\mathcal{CA}_p$

Boundedness criteria for superposition, backward shift, and Schwarzian derivative operators

Extension of operator theory in the context of analytic Campanato spaces

Abstract

This article is devoted to not only characterizing the first and second preduals of the analytic Campanato spaces ($\mathcal{CA}_p)$ on the unit disk, but also investigating boundedness of three operators: superposition ($\mathsf{S}^\phi$); backward shift ($\mathsf{S_b}$); Schwarzian derivative ($\mathsf{S}$), acting on $\mathcal{CA}_p$.