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 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 …

The present work has as a first goal to extend the previous results in Cazacu et al.(J Funct
Anal 283 (10): 109659, 2022) to weighted uncertainty principles with nontrivial radially …

We use a suitable transform related to Sobolev inequality to investigate the sharp constants
and optimizers for some Caffarelli-Kohn-Nirenberg-type inequalities which are related to the …

This paper focuses on optimal constants and optimizers of the second order Caffarelli-Kohn-
Nirenberg inequalities. Firstly, we aim to study optimal constants and optimizers for the …

In this paper we study the large time asymptotic behaviour of the heat equation with Hardy
inverse-square potential on corner spaces RN− k×(0,∞) k, k≥ 0. We first show a new …

When studying the weighted Hardy-Rellich inequality in $ L^ 2$ with the full gradient
replaced by the radial derivative the best constant becomes trivially larger or equal than in …

A simple proof of the refined sharp weighted Caffarelli-Kohn-Nirenberg inequalities Page 1
http://www.aimspress.com/journal/Math AIMS Mathematics, 8(11): 27983–27988. DOI …

In this paper we study the large time asymptotic behaviour of the heat equation with Hardy
inverse-square potential on corner spaces $\mathbb {R}^{Nk}\times (0,\infty)^ k $, $ k\geq …