A Restriction Theorem for M\'etivier Groups

In the spirit of an earlier result of M\"uller on the Heisenberg group we prove a restriction theorem on a certain class of two step nilpotent Lie groups. Our result extends that of M\"uller also in the framework of the Heisenberg group.Comment: Corrected typos, introduction revised. Final version, to appear in Advances in Mathematic

The Levi Decomposition of a Graded Lie Algebra

We show that a graded Lie algebra admits a Levi decomposition that is compatible with the grading

On derivations of subalgebras of real semisimple Lie algebras

Let g be a real semisimple Lie algebra with Iwasawa decomposition k+a+n. We show that, except for some explicit exceptional cases, every derivation of the nilpotent subalgebra n that preserves its restricted root space decomposition is of the form ad( W), where W belongs to m+a

The maximal operator of a normal Ornstein--Uhlenbeck semigroup is of weak type (1,1)

Consider a normal Ornstein\u2013Uhlenbeck semigroup in R^n, whose co- variance is given by a positive definite matrix. The drift matrix is assumed to have eigenvalues only in the left half-plane. We prove that the associated maximal operator is of weak type (1, 1) with respect to the invariant measure. This extends earlier work by G. Mauceri and L. Noselli. The proof goes via the special case where the matrix defining the covariance is I and the drift matrix is diagonal

From refined estimates for spherical harmonics to a sharp multiplier theorem on the Grushin sphere

We prove a sharp multiplier theorem of Mihlin-H\"ormander type for the Grushin operator on the unit sphere in $\mathbb{R}^3$, and a corresponding boundedness result for the associated Bochner-Riesz means. The proof hinges on precise pointwise bounds for spherical harmonics.Comment: 32 page

On the maximal operator of a general Ornstein-Uhlenbeck semigroup

If $Q$ is a real, symmetric and positive definite $n\times n$ matrix, and $B$ a real $n\times n$ matrix whose eigenvalues have negative real parts, we consider the Ornstein--Uhlenbeck semigroup on $\mathbb{R}^n$ with covariance $Q$ and drift matrix $B$. Our main result says that the associated maximal operator is of weak type $(1,1)$ with respect to the invariant measure. The proof has a geometric gist and hinges on the "forbidden zones method" previously introduced by the third author.Comment: 21 pages. Introduction revised. Some changes in Sections 3 and

On the norms of quaternionic harmonic projection operators

As a consequence of integral bounds for three classes of quaternionic spherical harmon-ics, we prove some bounds from below for the (Lp,L2) norm of quaternionic harmonic projectors, for p between 1 and 2