A note on partially hypoelliptic operators

Spectral Properties of Hypoelliptic Operators

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...

Semilinear Hypoelliptic Differential Operators with Multiple Characteristics

In this paper we consider the regularity of solutions of semilinear differential equations principal parts of which consist of linear polynomial operators constructed from real vector fields. Based on the study of fine properties of the principal linear parts we then obtain the regularity of solutions of the nonlinear equations. Some results obtained in this article are also new in the frame of...

A Note on Weighted Composition Operators on L^p-Spaces

H∞-calculus for Hypoelliptic Pseudodifferential Operators

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

Some Remarks on Degenerate Hypoelliptic Ornstein-uhlenbeck Operators

We study degenerate hypoelliptic Ornstein-Uhlenbeck operators in L spaces with respect to invariant measures. The purpose of this article is to show how recent results on general quadratic operators apply to the study of degenerate hypoelliptic Ornstein-Uhlenbeck operators. We first show that some known results about the spectral and subelliptic properties of Ornstein-Uhlenbeck operators may be...