Extrapolation of function spaces and related topics. (Q2846684)

The authors survey some results on extrapolation theory introduced by \textit{S. Yano} in [J. Math. Soc. Jpn. 3, 296--305 (1951; Zbl 0045.17901)]. The authors concentrate on Lorentz-Zygmund and Lipschitz spaces which can be obtained by extrapolation. They study their equivalent characterization and further properties. Moreover, they describe a method of extrapolation and its connection with limiting embeddings. In the last sections, the authors discuss some properties of Sobolev and Besov spaces.NEWLINENEWLINEIn this paper, only some ideas of proofs are given, and it is described how to deal with such questions. In special cases, the authors refer to the original papers for details.NEWLINENEWLINEFor the entire collection see [Zbl 1262.35002].