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April 2020 Homogeneous Besov spaces
Yoshihiro Sawano
Kyoto J. Math. 60(1): 1-43 (April 2020). DOI: 10.1215/21562261-2019-0038

Abstract

This note is based on a series of lectures delivered at Kyoto University in 2015. This note surveys the homogeneous Besov space B˙pqs on Rn with 1p, q and sR in a rather self-contained manner. Among other results, we show that S' and S'/P are isomorphic, and we also discuss the realizations in B˙pqs. The fact that S' and S'/P are isomorphic can be found in textbooks. The realization of B˙pqs 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.

Citation

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Yoshihiro Sawano. "Homogeneous Besov spaces." Kyoto J. Math. 60 (1) 1 - 43, April 2020. https://doi.org/10.1215/21562261-2019-0038

Information

Received: 6 February 2016; Revised: 8 December 2016; Accepted: 10 November 2017; Published: April 2020
First available in Project Euclid: 18 December 2019

zbMATH: 07194826
MathSciNet: MR4065179
Digital Object Identifier: 10.1215/21562261-2019-0038

Subjects:
Primary: 42B35
Secondary: 46A04

Rights: Copyright © 2020 Kyoto University

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Vol.60 • No. 1 • April 2020
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