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A remark on the constants of the Littlewood-Paley inequality

Author: S. K. Pichorides
Journal: Proc. Amer. Math. Soc. 114 (1992), 787-789
MSC: Primary 42A50; Secondary 30D55
MathSciNet review: 1088445
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Abstract: If $ f \in {H^p},p > 1$, and $ \gamma $ denotes its Littlewood-Paley square function, then $ \vert\vert\gamma \vert{\vert _p} \leq {B_p}\vert\vert f\vert{\vert _p}$ with $ {B_p} = 0({(p - 1)^{ - 1}}),p \to {1^ + }$.

References [Enhancements On Off] (What's this?)

  • [B] J. Bourgain, On the behavior of the constant in the Littlewood-Paley inequality, Lecture Notes in Math., no. 1376, Springer-Verlag, Berlin and New York, 1989, pp. 202-208. MR 1008724 (90g:26010)
  • [C] L. Carleson, On the Littlewood-Paley theorem, Institute Mittag-Leffler, 1967.
  • [P] S. Pichorides, On the Littlewood-Paley square function inequality, Colloq. Math. 60/61 (1990), 687-691. MR 1096408 (93b:26029)
  • [Z] A. Zygmund, Trigonometric series, I, II, Cambridge Univ. Press, London and New York, 1968. MR 0236587 (38:4882)

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