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Paley's Inequality for the Jacobi Expansions
Author(s) -
Kanjin Yuichi,
Sato Kunio
Publication year - 2001
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1017/s0024609301008098
Subject(s) - mathematics , inequality , unit (ring theory) , function (biology) , pure mathematics , mathematical analysis , mathematics education , biology , evolutionary biology
Let F ( z ) = ∑ n = 0 ∞a n z nbe an analytic function in the unit disc satisfyingsup 0 < r < 1∫ 0 2 π| F ( r e i θ) | d θ < ∞ .Then(∑ k = 1 ∞ | a 2 k| 2 )1 / 2 < ∞ . , which is familiar as Paley's inequality. In this paper, an analogue of this inequality with respect to the Jacobi expansions is established.