First Order Hardy Inequalities Revisited (Communications in Mathematical Research, 2022)
In this paper, we consider the first order Hardy inequalities usingsimple equalities. This basic setting not only permits to derive quickly manywell-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 edgeLaplacian, or the Grushin type operator.
Keywords: First order Hardy inequality; inequality via equality; generalized Bessel pair.