Abstract
ABSTRACTIn this paper, we derive a sufficient condition on a pair of nonnegative weight functions and w in so that the general weighted Hardy type inequality with a remainder termholds for all . Here and is the sub-elliptic gradient. It is worth emphasizing here that our unifying method may be readily used to recover most of the previously known sharp weighted Hardy and Heisenberg–Pauli–Weyl type inequalities as well as to construct other new inequalities with an explicit constant. Furthermore, we also obtain new results on two-weight Hardy type inequalities with remainder terms on smooth bounded domains in via a non-linear partial differential inequality.
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