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Sur la séparation régulière. (Regular separation). (French) Zbl 0612.32008
The author proves the following version of the type of inequalities, which are named by Hörmander and himself.
Theorem: Let A be relatively compact subanalytic in an analytic variety V and let \(\phi\),\(\psi\) : \(A\to {\mathbb{R}}\) be continuous and subanalytic. If \(\{\phi =0\}\subset \{\psi =0\}\), then \(| \psi (x)| \leq c | \phi (x)|^{\alpha}\) on A for some \(c,\alpha >0.\)
First it is shown, that a subanalytic set which is contained in a semianalytic set of dim\(\leq 2\) is itself semianalytic. This is applied for the image of A in \({\mathbb{R}}^ 2\) under (\(\phi\),\(\psi)\); from which the Theorem follows in the usual way.
Reviewer: H.-J.Nastold

32B20 Semi-analytic sets, subanalytic sets, and generalizations
32C05 Real-analytic manifolds, real-analytic spaces
58A07 Real-analytic and Nash manifolds