This open access book provides an extensive treatment of Hardy inequalities and closely
related topics from the point of view of Folland and Stein's homogeneous (Lie) groups. The …

In this paper, we present a version of horizontal weighted Hardy–Rellich type and Caffarelli–
Kohn–Nirenberg type inequalities on stratified groups and study some of their …

We propose the analogues of boundary layer potentials for the sub-Laplacian on
homogeneous Carnot groups/stratified Lie groups and prove continuity results for them. In …

Factorizations and Hardy and Hardy–Rellich inequalities Page 1 J. Spectr. Theory 10 (2020),
1277–1302 DOI 10.4171/JST/327 Journal of Spectral Theory © European Mathematical …

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 …

In this paper we complete the study started in [P. Pucci, L. Temperini, Existence for (p, q)
critical systems in the Heisenberg group, Adv. Nonlinear Anal. 9 (2020), 895-922] on some …

arXiv:2408.00013v2 [math.AP] 27 Sep 2024 Page 1 arXiv:2408.00013v2 [math.AP] 27 Sep 2024
FACTORIZATIONS AND POWER WEIGHTED RELLICH AND HARDY–RELLICH-TYPE …

In this note, we give several characterizations of weights for two-weight Hardy inequalities to
hold on general metric measure spaces possessing polar decompositions. Since there may …

In 1961, Birman proved a sequence of inequalities {I n}, for n∈ N, valid for functions in C 0 n
((0,∞))⊂ L 2 ((0,∞)). In particular, I 1 is the classical (integral) Hardy inequality and I 2 is the …