Orbital theory for affine Lie algebras.
Orthogonal symmetric pairs and the Rouvière isomorphism. (Paires symétriques orthogonales et isomorphisme de Rouvière.)
Orthogonality within the families of -, -, and -functions of any compact semisimple Lie group.
Oscillating multipliers on the Heisenberg group
Let ℒ be the sublaplacian on the Heisenberg group Hⁿ. A recent result of Müller and Stein shows that the operator is bounded on for all p satisfying |1/p - 1/2| < 1/(2n). In this paper we show that the same operator is bounded on in the bigger range |1/p - 1/2| < 1/(2n-1) if we consider only functions which are band limited in the central variable.
Pluriharmonic functions on symmetric tube domains with BMO boundary values
Let 𝓓 be a symmetric Siegel domain of tube type and S be a solvable Lie group acting simply transitively on 𝓓. Assume that L is a real S-invariant second order operator that satisfies Hörmander's condition and annihilates holomorphic functions. Let H be the Laplace-Beltrami operator for the product of upper half planes imbedded in 𝓓. We prove that if F is an L-Poisson integral of a BMO function and HF = 0 then F is pluriharmonic. Some other related results are also considered.
Poincaré series and Kloosterman sums for SL(3, Z)
Pointwise estimates for densities of stable semigroups of measures
Let be a symmetric α-stable semigroup of probability measures on a homogeneous group N, where 0 < α < 2. Assume that are absolutely continuous with respect to Haar measure and denote by the corresponding densities. We show that the estimate , x≠0, holds true with some integrable function Ω on the unit sphere Σ if and only if the density of the Lévy measure of the semigroup belongs locally to the Zygmund class LlogL(N╲e). The problem turns out to be related to the properties of the maximal...
Pointwise estimates for the Poisson kernel on NA groups by the Ancona method
Poisson Integrals and Boundary Components of Symmetric Spaces.
Poisson kernels and pluriharmonic -functions on homogeneous Siegel domains.
Pompeiu Sets in Compact Heisenberg Manifolds.
Prehomogeneous spaces associated with nilpotent orbits in simple real Lie algebras and and their relative invariants.
Primitive Ideals and Orbital Integrals in Complex Classical Groups.
Progrès récents vers la classification du dual unitaire des groupes réductifs réels
Propagation des singularités sur des groupes de Lie nilpotents
Properties of centered random walks on locally compact groups and Lie groups.
Pseudodifferential Operators on SU(2).
Radon-Transformation auf nilpotenten Lie-Gruppen.
Recent developments in the theory of function spaces
Rectifiability and perimeter in step 2 Groups
We study finite perimeter sets in step 2 Carnot groups. In this way we extend the classical De Giorgi’s theory, developed in Euclidean spaces by De Giorgi, as well as its generalization, considered by the authors, in Heisenberg groups. A structure theorem for sets of finite perimeter and consequently a divergence theorem are obtained. Full proofs of these results, comments and an exhaustive bibliography can be found in our preprint (2001).