Michel Marias

H1-boundedness of Riesz transforms and imaginary powers of the Laplacian on Riemannian manifolds

We prove that the linearized Riesz transforms and the imaginary powers of the Laplacian areH1-bounded on complete Riemannian manifolds satisfying the doubling property and the Poincaré inequality, whereH1 denotes the Hardy space onM.

Hr-bounds for spectral multipliers on graphs

We study the boundedness on the Hardy spaces H p of spectral multiplier operators associated with the discrete Laplacian on a weighted graph. We assume that the graph satisfies the doubling volume property and a Poincare inequality. We prove that there is p 0 ∈ (0,1), depending on the geometry of the graph, such that if the multiplier satisfies a condition similar to the one we have in the classical Hormander multiplier theorem, then the corresponding operator is bounded on H p , p ∈ (p 0 , 1].

bounds for spectral multipliers on graphs

We prove that certain spectral multipliers associated with the discrete Laplacian on graphs satisfying the doubling volume property and the Poincare inequality are bounded on the Hardy space H 1 .

Universal Taylor series on open subsets of Rn

In the case of the complex plane, several notions of universal Taylor series have been introduced, ([10, 2, 19, 20]). The purpose of the present article is to establish the existence of universal Taylor series of C∞ functions in general open subsets of the Euclidean space Rn, n ≥ 1.

Eigenfunctions of the Laplacian on rotationally symmetric manifolds

Eigenfunctions of the Laplacian on a negatively curved, rotationally symmetric manifold M = (Rn, ds2), ds2 = dr2+f(r)2dθ2, are constructed explicitly under the assumption that an integral of f(r) converges. This integral is the same one which gives the existence of nonconstant harmonic functions on M.

Spectral theory for manifolds of hyperbolic type

For a class of (n+1)-dimensional manifolds of hyperbolic type, the spectral measure is described in terms of Poisson kernels. This implies that the spectrum is absolutely continuous and it is contained in [n 2 =4; +1).

Eigenfunctions of the Laplacian and boundary behaviour on manifolds of hyperbolic type

We describe a method of constructing explicitly eigenfunctions of the Laplacian with a prescribed boundary behaviour on a class of manifolds of hyperbolic type. These are manifolds of the form M fl X‹R◊ , where X is an n-dimensional Riemannian manifold and the metric of M is a perturbation of the hyperbolic one.

L^p estimates on functions of Markov operators

We prove L p estimates for functions of Markov operators on a discrete measure space of superpolynomial volume growth.