Potential operators in variable exponent Lebesgue spaces: two-weight estimates.
Proper action on a homogeneous space of reductive type.
Quantum unique ergodicity for Eisenstein series on
In this paper we prove microlocal version of the equidistribution theorem for Wigner distributions associated to Eisenstein series on . This generalizes a recent result of W. Luo and P. Sarnak who proves equidistribution for . The averaged versions of these results have been proven by Zelditch for an arbitrary finite-volume surface, but our proof depends essentially on the presence of Hecke operators and works only for congruence subgroups of . In the proof the key estimates come from applying...
Random walks on the affine group of local fields and of homogeneous trees
The affine group of a local field acts on the tree (the Bruhat-Tits building of ) with a fixed point in the space of ends . More generally, we define the affine group of any homogeneous tree as the group of all automorphisms of with a common fixed point in , and establish main asymptotic properties of random products in : (1) law of large numbers and central limit theorem; (2) convergence to and solvability of the Dirichlet problem at infinity; (3) identification of the Poisson boundary...
Range of the horocyclic Radon transform on trees
In this paper we study the Radon transform on the set of horocycles of a homogeneous tree , and describe its image on various function spaces. We show that the functions of compact support on that satisfy two explicit Radon conditions constitute the image under of functions of finite support on . We extend these results to spaces of functions with suitable decay on , whose image under satisfies corresponding decay conditions and contains distributions on that are not defined pointwise....
Rearrangement and continuity properties of functions on spaces of homogeneous type
Regular variation on homogeneous cones
Remarks on random walks on semi simple Lie groups
Résolubilité sur un espace riemannien symétrique
Sampling of Band-Limited Vectors.
Scalar irreducibility of Eigenspace Representations associated to a symmetric space.
Semigroup actions on homogeneous spaces.
Semi-groupes de Feller invariants sur les espaces hyperboliques
Séries de Laurent des fonctions holomorphes dans la complexification d'un espace symétrique compact
Sharp maximal functions associated with approximations of the identity in spaces of homogeneous type and applications
In the context of the spaces of homogeneous type, given a family of operators that look like approximations of the identity, new sharp maximal functions are considered. We prove a good-λ inequality for Muckenhoupt weights, which leads to an analog of the Fefferman-Stein estimate for the classical sharp maximal function. As a consequence, we establish weighted norm estimates for certain singular integrals, defined on irregular domains, with Hörmander conditions replaced by some estimates which do...
Sharp pointwise estimate for the kernels of the semigroup generated by sums of even powers of vector fields on homogeneous groups
Singular integral operators with non-smooth kernels on irregular domains.
Let χ be a space of homogeneous type. The aims of this paper are as follows.i) Assuming that T is a bounded linear operator on L2(χ), we give a sufficient condition on the kernel of T such that T is of weak type (1,1), hence bounded on Lp(χ) for 1 < p ≤ 2; our condition is weaker then the usual Hörmander integral condition.ii) Assuming that T is a bounded linear operator on L2(Ω) where Ω is a measurable subset of χ, we give a sufficient condition on the kernel of T so that T is of weak type...
Singular integrals on homogeneous spaces and some problems of classical analysis
Small time heat kernel behavior on Riemannian complexes.
Smooth operators for the regular representation on homogeneous spaces
A necessary and sufficient condition for a bounded operator on , M a Riemannian compact homogeneous space, to be smooth under conjugation by the regular representation is given. It is shown that, if all formal ’Fourier multipliers with variable coefficients’ are bounded, then they are also smooth. In particular, they are smooth if M is a rank-one symmetric space.