We give sharp remainder terms of L p and weighted Hardy and Rellich inequalities on one
of most general subclasses of nilpotent Lie groups, namely the class of homogeneous …

In this paper we give an extension of the classical Caffarelli-Kohn-Nirenberg inequalities: we
show that for $1< p, q<\infty $, $0< r<\infty $ with $ p+ q\geq r $, $\delta\in [0, 1]\cap\left [\frac …

In this paper, we prove several new Hardy type inequalities (such as the weighted Hardy
inequality, weighted Rellich inequality, critical Hardy inequality and critical Rellich …

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 …

We prove L p-Caffarelli–Kohn–Nirenberg type inequalities on homogeneous groups, which
is one of most general subclasses of nilpotent Lie groups, all with sharp constants. We also …

We provide the necessary and sufficient characterizations on a pair of positive radial
functions so that the two-weight Hardy inequalities hold true on homogeneous groups, one …

We analyze local (central) Morrey spaces, generalized local (central) Morrey spaces and
Campanato spaces on homogeneous groups. The boundedness of the Hardy-Littlewood …

In this paper we present a unified simple approach to anisotropic Hardy inequalities in
various settings. We consider Hardy inequalities which involve a Finsler distance from a …

In this paper, we prove the following reversed Hardy-Littlewood-Sobolev inequality with
extended kernel\begin {equation*}\int_ {\mathbb {R} _+^ n}\int_ {\partial\mathbb {R} …

We prove a range of critical Hardy inequalities and uncertainty type principles on one of
most general subclasses of nilpotent Lie groups, namely the class of homogeneous groups …