Sobolev-Gagliardo-Nirenberg and Markov type inequalities on subanalytic domains
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Desingularization and anL p -version of Glaeser-type estimates. In fact we obtain a bounds<-2d+1, whered is the maximal order of vanishing of the jacobian of the desingularization map of the domain.
Interpolation type inequalities for norms of functions and Bernstein-Markov type inequalities for multivariate polynomials (classical analysis).
Geometric criteria for the validity of local Markov inequalities (local analysis of the singularities of domains).
Multivariate Approximation Theory.
Thus our approach brings together the calculus of Glaeser-type estimates from differential analysis, the algebra of desingularization, the geometry of Markov type inequalities and the analysis of Sobolev-Nirenberg type estimates. Our exposition takes into account this interdisciplinary nature of the methods we exploit and is almost entirely self-contained. /lt>
KeywordsType Inequality Local Form Maximal Order Type Estimate Supremum Norm
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