Homogeneous Besov spaces

Abstract

This note is based on a series of lectures delivered in Kyoto University. This note surveys the homogeneous Besov space ${\dot{B}}_{pq}^s$ on ${\mathbb{R}}^n$ with $1\le p,q\le \infty$ and $s\in \mathbb{R}$ in a rather self-contained manner. Possible extensions of this type of function spaces are breifly discussed in the end of this article. In particular, the fundamental properties are stated for the spaces ${\dot{B}}_{pq}^s$ with $0<p,q\le \infty$ and $s\in \mathbb{R}$ and ${\dot{F}}_{pq}^s$ with $0<p<\infty$, $0<q\le \infty$ and $s\in \mathbb{R}$ as well as nonhomogeneous coupterparts $B_{pq}^s$ with $0<p,q\le \infty$ and $s\in \mathbb{R}$ and $F_{pq}^s$ with $0<p<\infty$, $0<q\le \infty$ and $s\in \mathbb{R}$.

32pages

References in corpus (3)

• Generalized Morrey spaces and trace operator
• Wavelet transforms for homogeneous mixed-norm Triebel--Lizorkin spaces
• Rough differential equations driven by signals in Besov spaces