Proceedings of the Japan Academy, Series A, Mathematical Sciences

New proofs of the trace theorem of Sobolev spaces

Yoichi Miyazaki

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Abstract

We present three new proofs of the trace theorem of $L_{p}$ Sobolev spaces, which do not rely on the theory of interpolation spaces. The first method originates in Morrey’s proof for the Sobolev embedding theorem concerning the Hölder-Zygmund space. The second method is based on Muramatu’s integral formula and the third method is based on an integral operator with Gauss kernel. These methods give unified viewpoints for the proofs of the trace theorem and the Sobolev embedding theorem.

Article information

Source
Proc. Japan Acad. Ser. A Math. Sci., Volume 84, Number 7 (2008), 112-116.

Dates
First available in Project Euclid: 17 July 2008

Permanent link to this document
https://projecteuclid.org/euclid.pja/1216308252

Digital Object Identifier
doi:10.3792/pjaa.84.112

Mathematical Reviews number (MathSciNet)
MR2450062

Zentralblatt MATH identifier
1170.46034

Subjects
Primary: 46E35: Sobolev spaces and other spaces of "smooth" functions, embedding theorems, trace theorems

Keywords
Sobolev space Besov space trace theorem Sobolev embedding theorem

Citation

Miyazaki, Yoichi. New proofs of the trace theorem of Sobolev spaces. Proc. Japan Acad. Ser. A Math. Sci. 84 (2008), no. 7, 112--116. doi:10.3792/pjaa.84.112. https://projecteuclid.org/euclid.pja/1216308252


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