The pseudoanalytic extensions for some spaces of analytic functions
Guanlong Bao, Hasi Wulan, Fangqin Ye

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 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, and the Dirichlet space.
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Taxonomy
TopicsHolomorphic and Operator Theory · Algebraic and Geometric Analysis · Mathematical Analysis and Transform Methods
