Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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, Geometric aspects of functional analysis (1987–88), Lecture Notes in Math., vol. 1376, Springer, Berlin, 1989, pp. 202–208. MR 1008724, 10.1007/BFb0090056
  • [C] L. Carleson, On the Littlewood-Paley theorem, Institute Mittag-Leffler, 1967.
  • [P] S. K. Pichorides, A note on the Littlewood-Paley square function inequality, Colloq. Math. 60/61 (1990), no. 2, 687–691. MR 1096408
  • [Z] A. Zygmund, Trigonometric series: Vols. I, II, Second edition, reprinted with corrections and some additions, Cambridge University Press, London-New York, 1968. MR 0236587

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 42A50, 30D55

Retrieve articles in all journals with MSC: 42A50, 30D55


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1992-1088445-6
Article copyright: © Copyright 1992 American Mathematical Society