2021/02/28 by Michael Ruzhansky, Daulti Verma
Mathematics · Physics and Astronomy · #Advanced Harmonic Analysis Research #Characterization (materials science) #Combinatorics #Differentiable function #Geometric Analysis and Curvature Flows #Hadamard transform #Hardy space #Homogeneous #Inequality #Mathematical analysis #Mathematics #Measure (data warehouse) #Metric (unit) #Metric space #Nonlinear Partial Differential Equations #Pure mathematics #math-ph #math.AP #math.FA #math.MP #math.SP #msc:22E30 #msc:26D10
paper · pdf · doi:10.1098/rspa.2021.0136
18 pages; this is the second part to the paper arXiv:1806.03728. Final version, to appear in Proc. Royal Soc. A
openalex created_date 2021/02/15 · arxiv created 2021/05/11 · openalex publication_date 2021/06/01 · arxiv updated 2021/07/14 · openalex updated_date 2026/08/05
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.