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On the trace problem for Lizorkin–Triebel spaces with mixed norms

✍ Scribed by Jon Johnsen; Winfried Sickel

Publisher
John Wiley and Sons
Year
2008
Tongue
English
Weight
360 KB
Volume
281
Category
Article
ISSN
0025-584X

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✦ Synopsis

Abstract

The subject is traces of Sobolev spaces with mixed Lebesgue norms on Euclidean space. Specifically, restrictions to the hyperplanes given by x~1~ = 0 and x~n~ = 0 are applied to functions belonging to quasi‐homogeneous, mixed norm Lizorkin–Triebel spaces ; Sobolev spaces are obtained from these as special cases. Spaces admitting traces in the distribution sense are characterised up to the borderline cases; these are also covered in case x~1~ = 0. For x~1~ the trace spaces are proved to be mixed‐norm Lizorkin–Triebel spaces with a specific sum exponent; for x~n~ they are similarly defined Besov spaces. The treatment includes continuous right‐inverses and higher order traces. The results rely on a sequence version of Nikol'skij's inequality, Marschall's inequality for pseudodifferential operators (and Fourier multiplier assertions), as well as dyadic ball criteria. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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