Fractional order derivative characterizations of Besov-Morrey type spaces with applications

TL;DR

This paper characterizes Besov-Morrey type spaces using fractional derivatives via K-Carleson measures and explores applications to growth conditions of solutions to linear complex differential equations.

Contribution

It introduces a fractional derivative characterization of Besov-Morrey spaces and extends previous results, also applying these to growth conditions of differential equation solutions.

Findings

Fractional derivative characterization of Besov-Morrey spaces established.

Extension of Sun et al.'s results on fractional derivatives.

Sufficient conditions for solution growth in linear complex differential equations.

Abstract

On the one hand, the fractional order derivative characterization of the Besov-Morrey type space $B_{p}^{K}(s)$ is established by $K$-Carleson measures, and it was also shown that $f \in B_{p}^{K}(s_1) \Leftrightarrow f^{\left(\frac{s_2 - s_1}{p}\right)} \in B_{p}^{K}(s_2)$, which extended the results of Sun et al. on the fractional derivative of Morrey type space. On the other hand, some sufficient conditions for the growth of solutions to linear complex differential equations have been obtained by using $n$th derivative criterion.