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PALEY'S INEQUALITY FOR THE JACOBI EXPANSIONS

Published online by Cambridge University Press:  25 July 2001

YUICHI KANJIN  and
KUNIO SATO
YUICHI KANJIN
Affiliation:
Department of Mathematics, General Education Hall, Kanazawa University, Kanazawa 920-1192, Japan; kanjin@kenroku.kanazawa-u.ac.jp
KUNIO SATO
Affiliation:
Department of Basic Technology, Faculty of Engineering, Yamagata University, Yonezawa 992-8510, Japan; tj194@dipfr.dip.yz.yamagata-u.ac.jp
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Abstract

Let F(z) = [sum ]∞n=0anzn be an analytic function in the unit disc satisfying

[formula here]

Then [formula here], which is familiar as Paley's inequality. In this paper, an analogue of this inequality with respect to the Jacobi expansions is established.

Type
NOTES AND PAPERS
Information
Bulletin of the London Mathematical Society , Volume 33 , Issue 4 , July 2001 , pp. 483 - 491
Copyright
© The London Mathematical Society 2001

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