On the Relation between Amenability of Locally Compact Groups and the Norms of Convolution Operators.
On the Segal-Shale-Weil Representations and Harmonic Polynomials.
On the Symplectic Structure of Coadjoint Orbits of (Solvable) Lie Groups and Applications. I.
On weighted inequalities for operators of potential type
In this paper, we discuss a class of weighted inequalities for operators of potential type on homogeneous spaces. We give sufficient conditions for the weak and strong type weighted inequalities sup_{λ>0} λ|{x ∈ X : |T(fdσ)(x)|>λ }|_{ω}^{1/q} ≤ C (∫_{X} |f|^{p}dσ)^{1/p} and (∫_{X} |T(fdσ)|^{q}dω )^{1/q} ≤ C (∫_X |f|^{p}dσ )^{1/p} in the cases of 0 < q < p ≤ ∞ and 1 ≤ q < p < ∞, respectively, where T is an operator of potential type, and ω and σ are Borel measures on the homogeneous...
Opérateurs invariants sur un immeuble affine de type <>
Orbit closures of generic unipotent flows on homogeneous spaces of SL (3, IR).
Orthogonal symmetric pairs and the Rouvière isomorphism. (Paires symétriques orthogonales et isomorphisme de Rouvière.)
Oscillating multipliers on noncompact symmetric spaces.
Outer measures and weak type estimates of Hardy-Littlewood maximal operators.
-adic Whittaker functions and vector bundles on flag manifolds
Permanence of metric fractals.
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.
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 multipliers on weighted BMO spaces
Let E and F be spaces of real- or complex-valued functions defined on a set X. A real- or complex-valued function g defined on X is called a pointwise multiplier from E to F if the pointwise product fg belongs to F for each f ∈ E. We denote by PWM(E,F) the set of all pointwise multipliers from E to F. Let X be a space of homogeneous type in the sense of Coifman-Weiss. For 1 ≤ p < ∞ and for , we denote by the set of all functions such that , where B(a,r) is the ball centered at a and of...
Poisson Integrals and Boundary Components of Symmetric Spaces.
Poisson kernels and pluriharmonic -functions on homogeneous Siegel domains.
Poisson kernels of drifted Laplace operators on trees and on the half-plane
Starting with the computation of the appropriate Poisson kernels, we review, complement, and compare results on drifted Laplace operators in two different contexts: homogeneous trees and the hyperbolic half-plane.
Poisson Summation of Kirillov Orbits.
Pompeiu Sets in Compact Heisenberg Manifolds.
Pompeiu's problem on symmetric spaces.