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

Chen Lu, Mingjin Li, Jianren Long

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.

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

Abstract

On the one hand, the fractional order derivative characterization of the Besov-Morrey type space is established by -Carleson measures, and it was also shown that , 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 th derivative criterion.

Paper Structure

This paper contains 3 sections, 15 theorems, 89 equations.

Table of Contents

  1. Introduction
  2. Fractional order derivative characterization of Besov-Morrey type space $B_{p}^{K}(s)$
  3. Applications

Key Result

Theorem A

Suppose $K$ satisfies (1.2) for some $0 < \sigma < 2$ and $\frac{\sigma}{2} \leq s < \infty$. Then $f \in D_K^s$ if and only if is a $K$-Carleson measure.

Theorems & Definitions (18)

  • Theorem A
  • Theorem 2.1
  • Remark 2.1
  • corollary 2.2
  • Lemma 2.1
  • Lemma 2.2
  • Lemma 2.3
  • Lemma 2.4
  • Lemma 2.5
  • proof
  • ...and 8 more