Interpolation of weighted Sobolev spaces

Cwikel, Michael; Einav, Amit

Abstract

In this work we present a newly developed study of the interpolation of weighted Sobolev spaces by the complex method. We show that in some cases, one can obtain an analogue of the famous Stein–Weiss theorem for weighted Lp spaces. We consider an example which gives some indication that this may not be possible in all cases. Our results apply in cases which cannot be treated by methods in earlier papers about interpolation of weighted Sobolev spaces.

Citation

Cwikel, M., & Einav, A. (2019). Interpolation of weighted Sobolev spaces. Journal of Functional Analysis, 277(7), 2381-2441. https://doi.org/10.1016/j.jfa.2018.11.008

• Journal Article Type: Article
• Acceptance Date: Nov 14, 2018
• Online Publication Date: Nov 20, 2018
• Publication Date: Aug 6, 2019
• Deposit Date: Nov 16, 2020
• Journal: Journal of Functional Analysis
• Print ISSN: 0022-1236
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 277
• Issue: 7
• Pages: 2381-2441
• DOI: https://doi.org/10.1016/j.jfa.2018.11.008
• Public URL: https://durham-repository.worktribe.com/output/1285790