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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

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