Sharp bounds for composition with quasiconformal mappings in Sobolev spaces

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:451

Article

Oliva, Marcos¹  Prats, Marti¹ 

[1] Univ Autonoma Madrid ICMAT, Dept Matemat, Madrid, Spain

关键词: Sobolev spaces;    Fractional smoothness;    Quasiconformal mappings;    Composition operator;   

DOI  :  10.1016/j.jmaa.2017.02.016

来源: Elsevier

【 摘 要 】

Let phi be a quasiconformal mapping, and let T-phi be the composition operator which maps f to f o phi. Since 0 may not be bi-Lipschitz, the composition operator need not map Sobolev spaces to themselves. The study begins with the behavior of T-phi on L-P and W-1,W-p for 1 < p < infinity. This cases are well understood but alternative proofs of some known results are provided. Using interpolation techniques it is seen that compactly supported Bessel potential functions in H-s,H-P are sent to H-s,H-q whenever 0 < s < 1 for appropriate values of q. The techniques used lead to sharp results and they can be applied to Besov spaces as well. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free