Proceedings of the Japan Academy, Series A, Mathematical Sciences

New proofs of the trace theorem of Sobolev spaces

Yoichi Miyazaki

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

First available in Project Euclid: 17 July 2008

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

Sobolev space Besov space trace theorem Sobolev embedding theorem


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.

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