Ruzhansky Michael, Verma Daulti
Department of Mathematics, Imperial College London, 180 Queen's Gate, London SW7 2AZ, UK.
Department of Mathematics: Analysis, Logic and Discrete Mathematics, Ghent University, Ghent, Belgium.
Proc Math Phys Eng Sci. 2019 Mar;475(2223):20180310. doi: 10.1098/rspa.2018.0310. Epub 2019 Mar 6.
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 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 , on homogeneous groups, on hyperbolic spaces and on Cartan-Hadamard manifolds. We note that doubling conditions are not required for our analysis.
在本笔记中，我们给出了在具有极分解的一般度量测度空间上使双权Hardy不等式成立的权函数的几种特征描述。由于此类空间上可能不存在可微结构，因此这些不等式是按照Hardy原始不等式的精神以积分形式给出的。我们给出了在(\mathbb{R}^n)、齐次群、双曲空间和Cartan - Hadamard流形上得到新的加权Hardy不等式的例子。我们注意到我们的分析不需要双倍条件。
