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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

F. G. AVKHADIEV  and
K.-J. WIRTHS
F. G. AVKHADIEV
Affiliation:
Chebotarev Research Institute, Kazan State Uuniversity, 420008 Kazan, Russia; nina@dionis.kfti.kcn.ru
K.-J. WIRTHS
Affiliation:
Institut für Analysis, Technische Universität Braunschweig, D-38106 Braunschweig, Germany; k-j.wirths@tu-bs.de
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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]

Type
NOTES AND PAPERS
Information
Bulletin of the London Mathematical Society , Volume 33 , Issue 6 , November 2001 , pp. 695 - 700
Copyright
© The London Mathematical Society 2001

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