2018/06/30 by Michael Ruzhansky, Daulti Verma · 1 citation
Mathematics · #math.FA #math.AP #math.SP
paper · pdf · doi:10.1098/rspa.2018.0310
published as Proc. R. Soc. A, 475 (2019), 20180310, 15pp · 18 pages; typos have been corrected
arxiv created 2019/12/22 · arxiv updated 2019/12/24
In this note we give several characterisations 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. We give examples obtaining new weighted Hardy inequalities on \mathbb Rn, on homogeneous groups, on hyperbolic spaces, and on Cartan-Hadamard manifolds.