Banach Journal of Mathematical Analysis
- Banach J. Math. Anal.
- Volume 13, Number 2 (2019), 407-426.
Functional characterizations of trace spaces in Lipschitz domains
Soumia Touhami, Abdellatif Chaira, and Delfim F. M. Torres
Abstract
Using a factorization theorem of Douglas, we prove functional characterizations of trace spaces involving a family of positive self-adjoint operators. Our method is based on the use of a suitable operator by taking the trace on the boundary of a bounded Lipschitz domain and applying Moore–Penrose pseudoinverse properties together with a special inner product on . We also establish generalized results of the Moore–Penrose pseudoinverse.
Article information
Source
Banach J. Math. Anal., Volume 13, Number 2 (2019), 407-426.
Dates
Received: 21 August 2018
Accepted: 30 November 2018
First available in Project Euclid: 13 February 2019
Permanent link to this document
https://projecteuclid.org/euclid.bjma/1550048427
Digital Object Identifier
doi:10.1215/17358787-2018-0044
Mathematical Reviews number (MathSciNet)
MR3927880
Zentralblatt MATH identifier
07045465
Subjects
Primary: 46E35: Sobolev spaces and other spaces of "smooth" functions, embedding theorems, trace theorems
Secondary: 47A05: General (adjoints, conjugates, products, inverses, domains, ranges, etc.)
Keywords
Lipschitz domains trace spaces trace operators Moore–Penrose pseudoinverse
Citation
Touhami, Soumia; Chaira, Abdellatif; Torres, Delfim F. M. Functional characterizations of trace spaces in Lipschitz domains. Banach J. Math. Anal. 13 (2019), no. 2, 407--426. doi:10.1215/17358787-2018-0044. https://projecteuclid.org/euclid.bjma/1550048427


