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ASYMPTOTICALLY SHARP BOUNDS IN THE HARDY–LITTLEWOOD INEQUALITIES ON MEAN VALUES OF ANALYTIC FUNCTIONS
Published online by Cambridge University Press: 28 November 2001
Abstract
Let f be analytic in the unit disc, and let it belong to the Hardy space Hp, equipped with the usual norm ∥f∥p. It is known from the work of Hardy and Littlewood that for q > p, the constants
[formula here]
with the usual extension to the case where q = ∞, have C(p, q) < ∞ .The authors prove that
[formula here]
and
[formula here]
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- © The London Mathematical Society 2001