New proofs of the trace theorem of Sobolev spaces. (English) Zbl 1170.46034

Summary: We present three new proofs of the trace theorem for \(L_{p}\) Sobolev spaces, which do not rely on the theory of interpolation spaces. The first method originates in Morrey’s proof of 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.


46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
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