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PALEY'S INEQUALITY FOR THE JACOBI EXPANSIONS

Published online by Cambridge University Press:  25 July 2001

YUICHI KANJIN
Affiliation:
Department of Mathematics, General Education Hall, Kanazawa University, Kanazawa 920-1192, Japan; [email protected]
KUNIO SATO
Affiliation:
Department of Basic Technology, Faculty of Engineering, Yamagata University, Yonezawa 992-8510, Japan; [email protected]
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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
Copyright
© The London Mathematical Society 2001

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