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JOURNALS // Matematicheskie Trudy // Archive
Mat. Tr., 2009 Volume 12, Number 1, Pages 144–204 (Mi mt178)
This article is cited in 7 papers

A criterion for straightening of a Lipschitz surface in the Lizorkin–Triebel sense. I

A. I. Parfenov

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia

Abstract: We study the conditions when the trace of a Lizorkin–Triebel space on a Lipschitz surface coincides with the trace of this space on a hyperplane. A criterion in terms of a dyadic weighted inequality is found for a wide range of indices.

Key words: Lipschitz domain, dyadic cube, trace, straightening, Lizorkin–Triebel space.

UDC: 517.518.234

Received: 08.05.2008


 English version: Siberian Advances in Mathematics, 2010, 20:2, 83–127

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© Steklov Math. Inst. of RAS, 2024