Hörmander's operators are an important class of linear elliptic-parabolic degenerate partial
differential operators with smooth coefficients, which have been intensively studied since the …

We prove local refined versions of Hardy's and Rellich's inequalities as well as of uncertainty
principles for sums of squares of vector fields on bounded sets of smooth manifolds under …

Many more results have been proved in the literature for operators without the drift term
(“sum of squares” of Hörmander type) than for complete Hörmander's operators. On the …

We consider operators of the form L=∑ ni= 1 X2 i+ X0 in a bounded domain of Rp where X0,
X1,..., Xn are nonsmooth Hörmander's vector fields of step r such that the highest order …

We introduce the concept of locally homogeneous space, and prove in this context L p and
C α estimates for singular and fractional integrals, as well as L p estimates on the …

We consider a family H:={X1,…, Xm} of vector fields in Rn. Under a suitable s-involutivity
assumption on commutators of order at most s, we show a ball-box theorem for Carnot …

Consider a family H:={X_j=:f_j⋅∇:j=1,...,m\} of C 1 vector fields in ℝ n and let s∈ ℕ. We
assume that for all p∈ 1,…, s and j 1,…, jp∈ 1,…, m the horizontal derivatives …

This is the text prepared for a minicourse held at Ghent University (Belgium) on January 8-
10, 2020, on the topic of Rothschild-Stein lifting and approximation theorem, originally …

In this note we discuss the relationship, under an algebraic constant rank condition, between
the regularity of the characteristic form's coefficients of a degenerate elliptic linear PDO in …

We describe classes of local coordinates on the Carnot–Carathéodory spaces of lower
smoothness which permit the homogeneous approximation of quasimetrics and basis vector …