We set up a one-parameter family of inequalities that contains both the Hardy inequalities
(when the parameter is 1) and the Caffarelli-Kohn-Nirenberg inequalities (when the …

We establish a general identity (Theorem 1.2) that implies both the $ L^{p} $-Hardy identities
and the $ L^{p} $-Caffarelli-Kohn-Nirenberg identities (Theorems 1.3 and 1.4) and $ L^{p} …

We establish sharpened forms of the Hardy type identities and inequalities which are
substantial improvements of Hardy inequalities for the operators− Δ H−(N− 1) 2 4 on the …

We study the Hardy identities and inequalities on Cartan-Hadamard manifolds using the
notion of a Bessel pair. These Hardy identities offer significantly more information on the …

In this paper we establish general weighted Hardy identities for several subelliptic settings
including Hardy identities on the Heisenberg group, Carnot groups with respect to a …

We study Hardy inequalities for $ p $-Schr\" odinger operators on general weighted graphs.
Specifically, we prove a Maz'ya-type result, where we characterize the space of Hardy …

The main purpose of this article is to establish the L p Hardy's identities and inequalities for
Dunkl operator on any finite balls and the entire space RN. We also prove Hardy's identities …

We investigate necessary and sufficient conditions on the weights for the Hardy-Rellich
inequalities to hold, and propose a new way to use the notion of Bessel pair to establish the …

We present a generic functional inequality on Riemannian manifolds, both in additive and
multiplicative forms, that produces well known and genuinely new Hardy-type inequalities …

Firstly, this paper establishes useful forms of the remainder term of Hardy-type inequalities
on general domains where the weights are functions of the distance to the boundary. For …