We prove results on the propagation of Gevrey and analytic wave front sets for a class of C∞ hypoelliptic equations with double characteristics.

We study hypoelliptic operators with polynomially bounded coefficients that are of the form K = ∑m i=1 X i Xi + X0 + f , where the Xj denote first order differential operators, f is a function with at most polynomial growth, and X i denotes the formal adjoint of Xi in L. For any ε > 0 we show that an inequality of the form ‖u‖δ,δ ≤ C(‖u‖0,ε + ‖(K + iy)u‖0,0) holds for suitable δ and C which are...

In this paper we state an inhomogeneous Dirichlet problem for a class of linear partial diierential operators which are non-hypoelliptic. We prove uniqueness, existence and regularity results for its solutions.

Abstract We study ultradistributional boundary values of zero solutions a hypoelliptic constant coefficient partial differential operator $$P(D) = P(D_x, D_t)$$ P ( D ) = x ,...

In this article we provide global subelliptic estimates for the linearized inhomogeneous Boltzmann equation without angular cutoff, and show that some global gain in the spatial direction is available although the corresponding operator is not elliptic in this direction. The proof is based on a multiplier method and the so-called Wick quantization, together with a careful analysis of the symbol...

We establish the existence of a bounded H∞-calculus for a large class of hypoelliptic pseudodifferential operators on R and closed manifolds.

In this paper we define and study the Dunkl convolution product and the Dunkl transform on spaces of distributions on R. By using the main results obtained, we study the hypoelliptic Dunkl convolution equations in the space of distributions.

We announce some results obtained in a recent study [14], concerning a general class of hypoelliptic evolution operators in R. A Gaussian lower bound for the fundamental solution and a global Harnack inequality are given.