Hardy, weighted Trudinger-Moser and Caffarelli-Kohn-Nirenberg type inequalities on Riemannian manifolds with negative curvature

Ruzhansky, Michael; Yessirkegenov, Nurgissa

doi:10.1016/j.jmaa.2021.125795

Cited by 1 publication

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“…We can also refer to the recent open access book [15] devoted to Hardy, Rellich and other inequalities in the setting of nilpotent Lie groups. For inequalities of different types, see [16][17][18][19][20].…”

Section: Introductionmentioning

confidence: 99%

Hardy inequalities on metric measure spaces, II: the case p > q

Ruzhansky

Verma

2021

Proc. R. Soc. A.

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In this paper, we continue our investigations giving the characterization of weights for two-weight Hardy inequalities to hold on general metric measure spaces possessing polar decompositions. Since there may be no differentiable structure on such spaces, the inequalities are given in the integral form in the spirit of Hardy’s original inequality. This is a continuation of our paper (Ruzhansky & Verma 2018. Proc. R. Soc. A 475 , 20180310 ( doi:10.1098/rspa.2018.0310 )) where we treated the case p ≤ q . Here the remaining range p > q is considered, namely, 0 < q < p , 1 < p < ∞. We give several examples of the obtained results, finding conditions on the weights for integral Hardy inequalities on homogeneous groups, as well as on hyperbolic spaces and on more general Cartan–Hadamard manifolds. As in the first part of this paper, we do not need to impose doubling conditions on the metric.

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