Characterizations of Hardy-type, Bergman-type and Dirichlet-type spaces on certain classes of complex-valued functions

TL;DR

This paper characterizes Hardy-type, Bergman-type, and Dirichlet-type function spaces on specific classes of complex-valued functions and applies these results to nonlinear PDEs.

Contribution

It provides new characterizations of these function spaces and demonstrates their applications to solving nonlinear partial differential equations.

Findings

New characterizations of Hardy-type, Bergman-type, and Dirichlet-type spaces

Applications to nonlinear PDEs

Enhanced understanding of complex-valued function spaces

Abstract

In this paper, we continue our investigation of function spaces on certain classes of complex-valued functions. In particular, we give characterizations on Hardy-type, Bergman-type and Dirichlet-type spaces. Furthermore, we present applications of our results to certain nonlinear PDEs.