Marco Mughetti

Lower Bound Estimates Without Transversal Ellipticity

We study the validity of Hörmanders inequality for some classes of pseudo-differential operators for which the transversal ellipticity condition does not hold.

Gevrey Hypoellipticity for an Interesting Variant of Kohn’s Operator

In this paper we consider the analogue of Kohn’s operator but with a point singularity,

On the Generalization of Hörmander's Inequality

P = BB^* + B^* (t^{2\ell } + x^{2k} )B, B = D_x + ix^{q - 1} D_t .

A priori estimates for second order operators with symplectic characteristic manifold

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A counterexample to a lower bound for a class of pseudodifferential operators

We prove Feffermans SAK Principle for a class of hypoelliptic operators on R2 whose nonnegative symbol vanishes anisotropically on the characteristic manifold.

On the Cauchy Problem for a Class of Linear Weakly Hyperbolic Operators

ABSTRACT We are concerned with a lower bound with a gain of k/2 + 1 derivatives for the class OP N m, k (X, Σ) of pesudodifferential operators with characteristics of even multiplicity k ≥ 2. In the case of double characteristics operators (k = 2), we recapture a well-known inequality due to Hörmander.

Analytic Hypoellipticity for Sums of Squares and the Treves Conjecture

SuntoNel presente articolo si mostra come il calcolo pseudodifferenziale costruito da Boutet de Monvel possa essere esteso ad una classe di operatori ipoellittici con degenerazione anisotropa ed espresso in termini di una opportuna metrica di Weyl-Hörmander. Il calcolo sviluppato viene usato nella costruzione di una parametrice nella classe di operatori considerata.AbstractWe set Boutet de Monvels Calculus for hypoelliptic operators (in the case of flat symplectic characteristic manifold) in a Weyl-Hörmander framework that also contains anisotropically vanishing symbols. In this context we construct a parametrix for the related operators.

Hypoellipticity and nonhypoellipticity for sums of squares of complex vector fields

We prove Feffermans SAK Principle for a class of classical pseudodifferential operators on with symplectic characteristic manifold