A remark on the constants of the Littlewood-Paley inequality
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- by S. K. Pichorides PDF
- Proc. Amer. Math. Soc. 114 (1992), 787-789 Request permission
Abstract:
If $f \in {H^p},p > 1$, and $\gamma$ denotes its Littlewood-Paley square function, then $||\gamma |{|_p} \leq {B_p}||f|{|_p}$ with ${B_p} = 0({(p - 1)^{ - 1}}),p \to {1^ + }$.References
- J. Bourgain, On the behavior of the constant in the Littlewood-Paley inequality, Geometric aspects of functional analysis (1987–88), Lecture Notes in Math., vol. 1376, Springer, Berlin, 1989, pp. 202–208. MR 1008724, DOI 10.1007/BFb0090056 L. Carleson, On the Littlewood-Paley theorem, Institute Mittag-Leffler, 1967.
- S. K. Pichorides, A note on the Littlewood-Paley square function inequality, Colloq. Math. 60/61 (1990), no. 2, 687–691. MR 1096408, DOI 10.4064/cm-60-61-2-687-691
- A. Zygmund, Trigonometric series: Vols. I, II, Cambridge University Press, London-New York, 1968. Second edition, reprinted with corrections and some additions. MR 0236587
Additional Information
- © Copyright 1992 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 114 (1992), 787-789
- MSC: Primary 42A50; Secondary 30D55
- DOI: https://doi.org/10.1090/S0002-9939-1992-1088445-6
- MathSciNet review: 1088445