Displaying similar documents to “Theory of Bessel potentials. IV. Potentials on subcartesian spaces with singularities of polyhedral type”

Levi's forms of higher codimensional submanifolds

Andrea D'Agnolo, Giuseppe Zampieri (1991)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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Let X ≅ C n , let M be a C 2 hypersurface of X , S be a C 2 submanifold of M . Denote by L M the Levi form of M at z 0 ∈ S . In a previous paper [3] two numbers s ± ⁢ S , p , p ∈ T ˙ S * ⁢ X z 0 are defined; for S = M they are the numbers of positive and negative eigenvalues for L M . For S ⊂ M , p ∈ S × M T ˙ * S X ) , we show here that s ± ⁢ S , p are still the numbers of positive and negative eigenvalues for L M when restricted to T z 0 C ⁢ S . Applications to the concentration in degree for microfunctions at the boundary are given.

A Whitney extension theorem in L p and Besov spaces

Alf Jonsson, Hans Wallin (1978)

Annales de l'institut Fourier

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The classical Whitney extension theorem states that every function in Lip ( β , F ) , F ⊂ R n , F closed, k < β ≤ k + 1 , k a non-negative integer, can be extended to a function in Lip ( β , R n ) . Her Lip ( β , F ) stands for the class of functions which on F have continuous partial derivatives up to order k satisfying certain Lipschitz conditions in the supremum norm. We formulate and prove a similar theorem in the L p -norm. The restrictions to R d , d < n , of the Bessel potential spaces in R n and the Besov or generalized Lipschitz...

Module-valued functors preserving the covering dimension

Jan Spěvák (2015)

Commentationes Mathematicae Universitatis Carolinae

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We prove a general theorem about preservation of the covering dimension dim by certain covariant functors that implies, among others, the following concrete results. If G G is a pathwise connected...

Regularity properties of the equilibrium distribution

Hans Wallin (1965)

Annales de l'institut Fourier

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Soit F un sous-ensemble compact de R m ayant des points intérieurs et soit μ α F la distribution d’équilibre sur F de masse totale 1 par rapport au noyau r α - m avec 0 < α < 2 pour m ≥ 2 , et 0 < α < 1 pour m = 1 . La restriction de μ α F à l’intérieur de F est absolument continue et a pour densité f α F . On donne une formule explicite pour f α F et, pour une classe générale d’ensembles F , on démontre que f α F , définie en réalité sur un ensemble de mesure de Lebesgue nulle, croît comme la distance à la frontière ∂ F de F élevée à la puissance...

Maps with dimensionally restricted fibers

Vesko Valov (2011)

Colloquium Mathematicae

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We prove that if f: X → Y is a closed surjective map between metric spaces such that every fiber f - 1 ( y ) belongs to a class S of spaces, then there exists an F σ -set A ⊂ X such that A ∈ S and d i m f - 1 ( y ) ∖ A = 0 for all y ∈ Y. Here, S can be one of the following classes: (i) M: e-dim M ≤ K for some CW-complex K; (ii) C-spaces; (iii) weakly infinite-dimensional spaces. We also establish that if S = M: dim M ≤ n, then dim f ∆ g ≤ 0 for almost all g ∈ C ( X , n + 1 ) .

On signatures associated with ramified coverings and embedding problems

J. Wood, Emery Thomas (1973)

Annales de l'institut Fourier

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Given a cohomology class ξ ∈ H 2 ( M ; Z ) there is a smooth submanifold K ⊂ M Poincaré dual to ξ . A special class of such embeddings is characterized by topological properties which hold for nonsingular algebraic hypersurfaces in C P n . This note summarizes some results on the question: how does the divisibility of ξ restrict the dual submanifolds K in this class ? A formula for signatures associated with a d -fold ramified cover of M branched along K is given and a proof is included in case d = 2 .