The pseudoanalytic extensions for some spaces of analytic functions

TL;DR

This paper characterizes various spaces of analytic functions, including $Q_K$, Besov, and Morrey spaces, using pseudoanalytic extensions of primitive functions, with implications for classical Banach spaces.

Contribution

It introduces a novel characterization method for these function spaces via pseudoanalytic extensions, extending to classical Banach spaces.

Findings

Characterization of $Q_K$, Besov, and Morrey spaces using pseudoanalytic extensions.

Results applicable to classical Banach spaces like Bloch space, BMOA, and Dirichlet space.

Extension of characterization techniques to a broader class of analytic function spaces.

Abstract

Using the Cauchy-Riemann operator, we characterize $Q_K$ spaces, Besov spaces and analytic Morrey spaces in terms of pseudoanalytic extensions of primitive functions. Our results are also true on some classical Banach spaces, such as the Bloch space, $BMOA$ and the Dirichlet space.