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Using the Bessel pairs in the sense of Ghoussoub and Moradifam 16, we provide the necessary and sufficient conditions on a pair of positive functions so that the Hardy type inequalities in the spirit of Badiale-Tarantello 3 hold. We also set up the requirements for a pair of potentials so that the Hardy-Rellich type inequalities with radial derivatives are valid.
Nguyen Lam (Thu,) studied this question.
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