This note is based on a series of lectures delivered at Kyoto University in 2015. This note surveys the homogeneous Besov space on with , and in a rather self-contained manner. Among other results, we show that and are isomorphic, and we also discuss the realizations in . The fact that and are isomorphic can be found in textbooks. The realization of can be found in works by Bahouri, Chemin, and Danchin and by Bourdaud for example. Here, we prove these facts using fundamental results in functional analysis such as the Hahn–Banach extension theorem.
"Homogeneous Besov spaces." Kyoto J. Math. 60 (1) 1 - 43, April 2020. https://doi.org/10.1215/21562261-2019-0038