Abstract:
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We study the optimal bounds for the Hardy operator S minus the identity, as well as S and its dualoperator S*, on the full range 1 = p = 8, for the cases of decreasing, positive or general functions (infact, these two kinds of inequalities are equivalent for the appropriate cone of functions). For 1< p = 2, we prove that all these estimates are the same, but for 2 < p <8, they exhibit a completely different behavior. |