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July 2008 New proofs of the trace theorem of Sobolev spaces
Yoichi Miyazaki
Proc. Japan Acad. Ser. A Math. Sci. 84(7): 112-116 (July 2008). DOI: 10.3792/pjaa.84.112

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.

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Yoichi Miyazaki. "New proofs of the trace theorem of Sobolev spaces." Proc. Japan Acad. Ser. A Math. Sci. 84 (7) 112 - 116, July 2008. https://doi.org/10.3792/pjaa.84.112

Information

Published: July 2008
First available in Project Euclid: 17 July 2008

zbMATH: 1170.46034
MathSciNet: MR2450062
Digital Object Identifier: 10.3792/pjaa.84.112

Subjects:
Primary: 46E35

Keywords: Besov space , Sobolev embedding theorem , Sobolev space , trace theorem

Rights: Copyright © 2008 The Japan Academy

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Vol.84 • No. 7 • July 2008
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