论文标题
公制度量空间上的Hardy不平等，IV：案例$ p = 1 $
Hardy inequalities on metric measure spaces, IV: The case $p=1$
论文作者
论文摘要
在本文中，我们调查了公制测量空间的两重量不平等现象，该情况具有极地分解，$ p = 1 $和$ 1 \ leq q <\ infty。$这个结果补充了在\ cite {rv}中获得的强大不平等的情况。 $ p> 1的不平等现象为副产品，我们还获得了既定不平等的最佳常数。我们举例说明了均质谎言组，双曲线空间和cartan-hadamard歧管上的新加权强壮不平等的例子，$ p = 1 $和$ 1 \ le q <\ fy infty $。
In this paper, we investigate the two-weight Hardy inequalities on metric measure space possessing polar decompositions for the case $p=1$ and $1 \leq q <\infty.$ This result complements the Hardy inequalities obtained in \cite{RV} in the case $1< p\le q<\infty.$ The case $p=1$ requires a different argument and does not follow as the limit of known inequalities for $p>1.$ As a byproduct, we also obtain the best constant in the established inequality. We give examples obtaining new weighted Hardy inequalities on homogeneous Lie groups, on hyperbolic spaces and on Cartan-Hadamard manifolds for the case $p=1$ and $1\le q<\infty.$
