TY - JOUR
T1 - First Order Hardy Inequalities Revisited
AU - Huang , Xia
AU - Ye , Dong
JO - Communications in Mathematical Research 
VL - 4
SP - 535
EP - 559
PY - 2022
DA - 2022/10
SN - 38
DO - http://doi.org/10.4208/cmr.2021-0085
UR - https://global-sci.org/intro/article_detail/cmr/21071.html
KW - First order Hardy inequality, inequality via equality, generalized Bessel pair.
AB - <p style="text-align: justify;">In this paper, we consider the first order Hardy inequalities using
simple equalities. This basic setting not only permits to derive quickly many
well-known Hardy inequalities with optimal constants, but also supplies improved or new estimates in miscellaneous situations, such as multipolar potential, the exponential weight, hyperbolic space, Heisenberg group, the edge
Laplacian, or the Grushin type operator.</p>