We will illustrate how factorizations of singular, even-order partial
differential operators yield an elementary approach to classical
inequalities of Hardy-Rellich-type. More precisely, using this
factorization method, we will derive a general inequality and
demonstrate how particular choices of the parameters contained in this
inequality yield well-known inequalities, such as the classical Hardy
and Rellich inequalities, as special cases. Actually, other special
cases yield additional and apparently less well-known inequalities.
We will indicate that our method, in addition to being elementary, is
quite flexible when it comes to a variety of generalized situations
involving the inclusion of remainder terms and higher-order operators.
This is based on various joint work with Lance Littlejohn, I. Michael,
M. Pang, and R. Wellman.
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