Objects Dual to Subsemigroups of Groups.
On a Class of Generalized Gelfand Pairs.
On a zonal polynomial integral.
On convergence for the square root of the Poisson kernel in symmetric spaces of rank 1
Let P(z,β) be the Poisson kernel in the unit disk , and let be the λ -Poisson integral of f, where . We let be the normalization . If λ >0, we know that the best (regular) regions where converges to f for a.a. points on ∂ are of nontangential type. If λ =0 the situation is different. In a previous paper, we proved a result concerning the convergence of toward f in an weakly tangential region, if and p > 1. In the present paper we will extend the result to symmetric spaces X of...
On Deny's characterization of the potential kernel for a convolution Feller semi-group
The convolution kernels on a homogeneous space , where is a compact sub-group of , that satisfy the complete maximum principle are characterized.Deny’s result for abelian groups , but with a stronger hypothesis, is a special case.
On Eigenspaces of the Hecke Algebra with Respect to a Good Maximal Compact Subgroup of ap-Adic Reductive Group.
On fractional differentiation and integration on spaces of homogeneous type.
In this paper we define derivatives of fractional order on spaces of homogeneous type by generalizing a classical formula for the fractional powers of the Laplacean [S1], [S2], [SZ] and introducing suitable quasidistances related to an approximation of the identity. We define integration of fractional order as in [GV] but using quasidistances related to the approximation of the identity mentioned before.We show that these operators act on Lipschitz spaces as in the classical cases. We prove that...
On limit multiplicities of discrete series representations in spaces of automorphic forms.
On maximal functions over circular sectors with rotation invariant measures
Given a rotation invariant measure in , we define the maximal operator over circular sectors. We prove that it is of strong type for and we give necessary and sufficient conditions on the measure for the weak type inequality. Actually we work in a more general setting containing the above and other situations.
On mean periodic functions on complex hyperbolic spaces.
On molecules and fractional integrals on spaces of homogeneous type with finite measure
In this paper we prove the continuity of fractional integrals acting on nonhomogeneous function spaces defined on spaces of homogeneous type with finite measure. A definition of the molecules which are used in the theory is given. Results are proved for , , BMO, and Lipschitz spaces.
On positive Rockland operators
Let G be a homogeneous Lie group with a left Haar measure dg and L the action of G as left translations on . Further, let H = dL(C) denote a homogeneous operator associated with L. If H is positive and hypoelliptic on we prove that it is closed on each of the -spaces, p ∈ 〈 1,∞〉, and that it generates a semigroup S with a smooth kernel K which, with its derivatives, satisfies Gaussian bounds. The semigroup is holomorphic in the open right half-plane on all the -spaces, p ∈ [1,∞]. Further extensions...
On some causal and conformal groups.
On some dimension problems for self-affine fractals.
On some series of representations related to symmetric spaces
On s-sets and mutual absolute continuity of measures on homogeneous spaces.
On the causal structure of Lorentzian Lie groups. A globality theorem for Lorentzian cones in certain solvable Lie algebras.
On the Convergence and Divergence Behaviour of Approximation Processes in Homogeneous Banach Spaces.
On the Corwin-Greenleaf conjecture. (Sur la conjecture de Corwin-Greenleaf.)
On the exponential integrability of fractional integrals on spaces of homogeneous type
In this paper we show that the fractional integral of order α on spaces of homogeneous type embeds into a certain Orlicz space. This extends results of Trudinger [T], Hedberg [H], and Adams-Bagby [AB].