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In 1961, Birman proved a sequence of inequalities {In}, for n∈N, valid for functions in C0n((0,∞))⊂L2((0,∞)). In particular, I1 is the classical (integral) Hardy inequality and I2 is the well-known Rellich inequality. In this paper, we give a proof of this sequence of inequalities valid on a certain Hilbert space Hn([0,∞)) of functions defined on [0,∞). Moreover, f∈Hn([0,∞)) implies f′∈Hn−1([0,∞));...
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