In this paper we show a number of logarithmic inequalities on several classes of Lie groups:
log-Sobolev inequalities on general Lie groups, log-Sobolev (weighted and unweighted) …

In this article, we investigate spectral properties of the sublaplacian G on the Engel group,
which is the main example of a Carnot group of step 3. We develop a new approach to the …

In this paper we develop a theory of Besov and Triebel–Lizorkin spaces on general
noncompact connected Lie groups endowed with a sub-Riemannian structure. Such spaces …

The aim of this paper is to begin a systematic study of functional inequalities on symmetric
spaces of noncompact type of higher rank. Our first main goal of this study is to establish the …

We obtain a fractional Leibniz rule associated to bilinear Hermite pseudo-multipliers in the
context of Hermite Besov and Hermite Triebel–Lizorkin spaces. As a byproduct, we show …

We study the fractional Laplacian and the homogeneous Sobolev spaces on R^ d R d, by
considering two definitions that are both considered classical. We compare these different …

In this paper we estimate the Sobolev embedding constant on general noncompact Lie
groups, for sub-Riemannian inhomogeneous Sobolev spaces endowed with a left invariant …

In this paper we obtain two-weight Hardy inequalities on general metric measure spaces
possessing polar decompositions. Moreover, we also find necessary and sufficient …

We prove a local L p L^p‐Poincaré inequality, 1⩽ p<∞ 1\leqslantp<∞, on non‐compact Lie
groups endowed with a sub‐Riemannian structure. We show that the constant involved …

In this note we prove the anisotropic version of the Shannon inequality. This can be
conveniently realised in the setting of Folland and Stein's homogeneous groups. We give …