$p$-harmonic measure is not additive on null sets

José G. Llorente; Juan J. Manfredi; Jang-Mei Wu

Displaying similar documents to “ $p$ -harmonic measure is not additive on null sets”

On the boundary limits of harmonic functions with gradient in $L^{p}$

Yoshihiro Mizuta (1984)

Annales de l'institut Fourier

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This paper deals with tangential boundary behaviors of harmonic functions with gradient in Lebesgue classes. Our aim is to extend a recent result of Cruzeiro (C.R.A.S., Paris, 294 (1982), 71–74), concerning tangential boundary limits of harmonic functions with gradient in $L^{n} (R_{+}^{n})$ , $R_{+}^{n}$ denoting the upper half space of the $n$ -dimensional euclidean space $R^{n}$ . Our method used here is different from that of Nagel, Rudin and Shapiro (Ann. of Math., 116 (1982), 331–360); in fact, we use the integral representation...

Harmonic functions on the real hyperbolic ball I: Boundary values and atomic decomposition of Hardy spaces

Philippe Jaming (1999)

Colloquium Mathematicae

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We study harmonic functions for the Laplace-eltrami operator on the real hyperbolic space $_{n}$ . We obtain necessary and sufficient conditions for these functions and their normal derivatives to have a boundary distribution. In doing so, we consider different behaviors of hyperbolic harmonic functions according to the parity of the dimension of the hyperbolic ball $_{n}$ . We then study the Hardy spaces $H^{p} (_{n})$ , 0

Harnack inequalities for Schrödinger operators

Wolfhard Hansen (1999)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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On the axiomatic of harmonic functions I

Corneliu Constantinescu, A. Cornea (1963)

Annales de l'institut Fourier

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On présente quelques remarques sur l’axiomatique des fonctions harmoniques de M. Brelot. Ainsi, on montre qu’il est possible de remplacer dans l’axiome 3 l’ensemble ordonné filtrant des fonctions harmoniques par une suite monotone, et, s’il existe une fonction surharmonique positive alors : a) l’espace est la réunion d’un fermé polaire et d’un ouvert $σ$ -compact ; b) l’espace possède une base dénombrable s’il est localement à base dénombrable ; c) l’ensemble des composants...

On separately subharmonic functions (Lelong’s problem)

A. Sadullaev (2011)

Annales de la faculté des sciences de Toulouse Mathématiques

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The main result of the present paper is : every separately-subharmonic function $u (x, y)$ , which is harmonic in $y$ , can be represented locally as a sum two functions, $u = u^{*} + U$ , where $U$ is subharmonic and $u^{*}$ is harmonic in $y$ , subharmonic in $x$ and harmonic in $(x, y)$ outside of some nowhere dense set $S$ .

Hörmander systems and harmonic morphisms

Elisabetta Barletta (2003)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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Given a Hörmander system $X = {X_{1}, \dots, X_{m}}$ on a domain $Ω \subseteq 𝐑^{n}$ we show that any subelliptic harmonic morphism $φ$ from $Ω$ into a $ν$ -dimensional riemannian manifold $N$ is a (smooth) subelliptic harmonic map (in the sense of J. Jost & C-J. Xu, [9]). Also $φ$ is a submersion provided that $ν \leq m$ and $X$ has rank $m$ . If $Ω = 𝐇_{n}$ (the Heisenberg group) and $X = \{\frac{1}{2} (L_{α} + L_{\bar{α}}), \frac{1}{2 i} (L_{α} - L_{\bar{α}})\}$ , where $L_{\bar{α}} = \partial / \partial {\bar{z}}^{α} - i z^{α} \partial / \partial t$ is the Lewy operator, then a smooth map $φ : Ω \to N$ is a subelliptic harmonic morphism if and only if $φ \circ π : (C (𝐇_{n}), F_{θ_{0}}) \to N$ is a harmonic morphism, where $S^{1} \to C (𝐇_{n}) \overset{π}{\to} \to 𝐇_{n}$ is the canonical circle bundle and $F_{θ_{0}}$ ...

Displaying similar documents to “ p -harmonic measure is not additive on null sets”

On the boundary limits of harmonic functions with gradient in L p

Harmonic functions on the real hyperbolic ball I: Boundary values and atomic decomposition of Hardy spaces

Harnack inequalities for Schrödinger operators

On the axiomatic of harmonic functions I

On separately subharmonic functions (Lelong’s problem)

Hörmander systems and harmonic morphisms

Displaying similar documents to “ $p$ -harmonic measure is not additive on null sets”

On the boundary limits of harmonic functions with gradient in $L^{p}$