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Let $X$ be a metric space with a doubling measure, $Y$ be a boundedly compact metric space and $u : X \to Y$ be a Lebesgue precise mapping whose upper gradient $g$ belongs to the Lorentz space $L_{m, 1}$ , $m \geq 1$ . Let $E \subset X$ be a set of measure zero. Then ${\hat{ℋ}}_{m} (E \cap u^{- 1} (y)) = 0$ for $ℋ_{m}$ -a.e. $y \in Y$ , where $ℋ_{m}$ is the $m$ -dimensional Hausdorff measure and ${\hat{ℋ}}_{m}$ is the $m$ -codimensional Hausdorff measure. This property is closely related to the coarea formula and implies a version of the Eilenberg inequality. The result relies on estimates of Hausdorff content of level sets...

Coefficients généralisés de séries principales sphériques et distributions sphériques sur G.../G... .

P. Delorme (1991)

Inventiones mathematicae

Commutators of the Hardy-Littlewood maximal operator with BMO symbols on spaces of homogeneous type.

Hu, Guoen, Lin, Haibo, Yang, Dachun (2008)

Abstract and Applied Analysis

Compression Semigroups of Open Orbits on Real Flag Manifolds.

J. Hilgert, Karl-Hermann Neeb (1995)

Monatshefte für Mathematik

Conformally invariant trilinear forms on the sphere

Jean-Louis Clerc, Bent Ørsted (2011)

Annales de l’institut Fourier

To each complex number $λ$ is associated a representation $π_{λ}$ of the conformal group $S O_{0} (1, n)$ on $𝒞^{\infty} (S^{n - 1})$ (spherical principal series). For three values $λ_{1}, λ_{2}, λ_{3}$ , we construct a trilinear form on $𝒞^{\infty} (S^{n - 1}) \times 𝒞^{\infty} (S^{n - 1}) \times 𝒞^{\infty} (S^{n - 1})$ , which is invariant by $π_{λ_{1}} \otimes π_{λ_{2}} \otimes π_{λ_{3}}$ . The trilinear form, first defined for $(λ_{1}, λ_{2}, λ_{3})$ in an open set of $ℂ^{3}$ is extended meromorphically, with simple poles located in an explicit family of hyperplanes. For generic values of the parameters, we prove uniqueness of trilinear invariant forms.

Connection between the harmonic analysis on the sphere and the harmonic analysis on the one-sheeted hyperboloid: an analytic continuation viewpoint - I.

J. Bros, G.A. Viano (1996)

Forum mathematicum

Connection between the harmonic analysis on the sphere and the harmonic analysis on the one-sheeted hyperboloid: an analytic continuation viewpoint - II.

J. Bros, G.A. Viano (1996)

Forum mathematicum

Connection between the harmonic analysis on the sphere and the harmonic analysis on the one-sheeted hyperboloid: an analytic continuation viewpoint - III.

J. Bros, G.A. Viano (1997)

Forum mathematicum

Continuous measures on compact Lie groups

M. Anoussis, A. Bisbas (2000)

Annales de l'institut Fourier

We study continuous measures on a compact semisimple Lie group $G$ using representation theory. In Section 2 we prove a Wiener type characterization of a continuous measure. Next we construct central measures on $G$ which are related to the well known Riesz products on locally compact abelian groups. Using these measures we show in Section 3 that if $C$ is a compact set of continuous measures on $G$ there exists a singular measure $ν$ such that $ν * μ$ is absolutely continuous with respect to the Haar measure on...

Continuous Measures on Homogenous Spaces

Michael Björklund, Alexander Fish (2009)

Annales de l’institut Fourier

In this paper we generalize Wiener’s characterization of continuous measures to compact homogenous manifolds. In particular, we give necessary and sufficient conditions on probability measures on compact semisimple Lie groups and nilmanifolds to be continuous. The methods use only simple properties of heat kernels.

Convergence of Poisson integrals on semidirect extensions of homogeneous groups

Ewa Damek (1989)

Colloquium Mathematicae

Converse mean value theorems on trees and symmetric spaces.

Casadio Tarabusi, Enrico, Cohen, Joel M., Korányi, Adam, Picardello, Massimo A. (1998)

Journal of Lie Theory

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