On the Liouville property for sublaplacians

Italo Capuzzo Dolcetta; Alessandra Cutrì

Displaying similar documents to “On the Liouville property for sublaplacians”

Maximal functions related to subelliptic operators invariant under an action of a nilpotent Lie group

Ewa Damek (1992)

Studia Mathematica

Similarity:

Nilpotent Lie groups and eigenfunction expansions of Schrödinger operators II

Andrzej Hulanicki, Joe Jenkins (1987)

Studia Mathematica

Similarity:

Maximal functions related to subelliptic operators invariant under an action of a solvable Lie group

Ewa Damek, Andrzej Hulanicki (1991)

Studia Mathematica

Similarity:

On the domain S_a = {(x,e^b): x ∈ N, b ∈ ℝ, b > a} where N is a simply connected nilpotent Lie group, a certain N-left-invariant, second order, degenerate elliptic operator L is considered. N × {e^a} is the Poisson boundary for L-harmonic functions F, i.e. F is the Poisson integral F(xe^b) = ʃ_N f(xy)dμ^b_a(x), for an f in L^∞(N). The main theorem of the paper asserts that the maximal function M^a f(x) = sup{|ʃf(xy)dμ_a^b(y)| : b > a} is of weak type (1,1).

One dimensional symmetry in the Heisenberg group

Isabeau Birindelli, Jyotshana Prajapat (2001)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Similarity:

Liouville theorems for semilinear equations on the Heisenberg group

I. Birindelli, I. Capuzzo Dolcetta, A. Cutrì (1997)

Annales de l'I.H.P. Analyse non linéaire

Similarity:

Note on semigroups generated by positive Rockland operators on graded homogeneous groups

Jacek Dziubański, Waldemar Hebisch, Jacek Zienkiewicz (1994)

Studia Mathematica

Similarity:

Let L be a positive Rockland operator of homogeneous degree d on a graded homogeneous group G and let $p_{t}$ be the convolution kernels of the semigroup generated by L. We prove that if τ(x) is a Riemannian distance of x from the unit element, then there are constants c>0 and C such that $| p_{1} (x) | \leq C e x p (- c τ {(x)}^{d / (d - 1)})$ . Moreover, if G is not stratified, more precise estimates of $p_{1}$ at infinity are given.

On the definition of the dual Lie coalgebra of a Lie algebra.

Bertin Diarra (1995)

Publicacions Matemàtiques

Similarity:

Let L be a Lie algebra over a field K. The dual Lie coalgebra Lº of L has been defined by W. Michaelis to be the sum of all good subspaces V of the dual space L* of L: V is good if m(V) ⊂ V ⊗ V, where m is the multiplication of L. We show that Lº = m(L* ⊗ L*) as in the associative case.