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Function spaces for weighted subcoercive operators
Tommaso Bruno, Mattia Calzi, Marco M. Peloso
We develop a theory of Sobolev, Besov and Triebel--Lizorkin spaces associated with weighted subcoercive operators on any real connected Lie group.
Optimal heat kernel bounds and asymptotics on Damek--Ricci spaces
Tommaso Bruno, Federico Santagati
We give optimal bounds for the radial, space and time derivatives of arbitrary order of the heat kernel of the Laplace--Beltrami operator on Damek--Ricci spaces. In the case of sym…
Local and nonlocal Poincaré inequalities on Lie groups
Tommaso Bruno, Marco M. Peloso, Maria Vallarino
We prove a local -Poincaré inequality, , on noncompact Lie groups endowed with a sub-Riemannian structure. We show that the constant involved grows at most e…
Estimates for matrix coefficients of representations
Tommaso Bruno, Michael G. Cowling, Fabio Nicola +1
Estimates for matrix coefficients of unitary representations of semisimple Lie groups have been studied for a long time, starting with the seminal work by Bargmann, by Ehrenpreis a…
On the Riesz Transforms for the inverse Gauss measure
Tommaso Bruno, Peter Sjögren
Let be the absolutely continuous measure on whose density is the reciprocal of a Gaussian function. Let further be the natural self-adjoint La…
Potential spaces on Lie groups
Tommaso Bruno, Marco M. Peloso, Maria Vallarino
In this paper we discuss function spaces on a general noncompact Lie group, namely the scales of Triebel--Lizorkin and Besov spaces, defined in terms of a sub-Laplacian with drift.…