Paley's inequality for the Jacobi expansions
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概要
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Let F(z) = Σ∞n=0 anzn be an analytic function in the unit disc satisfying sup 0<r<1 ∫2π0 |F(reiθ)| dθ < ∞. Then (Σ∞k=1 |a2k|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.
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