A martingale inequality related to exponential square integrability
Author:
Jill Pipher
Journal:
Proc. Amer. Math. Soc. 118 (1993), 541546
MSC:
Primary 42B25
MathSciNet review:
1131038
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Abstract: We present an inequality for dyadic martingales (together with its continuous analog for functions on ) which is shown to be equivalent to a result of ChangWilsonWolff on exponential square integrability. The analog of this weighted inequality for double dyadic martingales is also proven. Finally, we discuss a possible connection between these inequalities and a theorem of Garnett.
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 S.Y. A. Chang, J. M. Wilson, and T. H. Wolff, Some weighted norm inequalities for the Schrödinger operator, Comment. Math. Helv. 60 (1985), 217246. MR 800004 (87d:42027)
 [2]
 R Coifman and C. Fefferman, Weighted norm inequalities for maximal functions and singular integrals, Studia Math. 51 (1974), 241250. MR 0358205 (50:10670)
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 B. E. J. Dahlberg, Approximation of harmonic functions, Ann. Inst. Fourier (Grenoble) 30 (1980), 97107. MR 584274 (82i:31010)
 [4]
 C. Fefferman and E. Stein, spaces of several variables, Acta Math. 129 (1972), 137192. MR 0447953 (56:6263)
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 J. Garnett, Two constructions in , Proc. Sympos. Pure Math., vol. 35, Amer. Math. Soc., Providence, RI, 1979, pp. 295301. MR 545269 (81d:30058)
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 J. Pipher, Bounded double square functions, Ann. Inst. Fourier (Grenoble) 36 (1986), 6982. MR 850744 (88h:42021)
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 J. M. Wilson, Weighted inequalities for the dyadic square function without dyadic , Duke Math. J. 55 (1987), 1950. MR 883661 (88d:42034)
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 , A sharp inequality for the square function, Duke Math. J. 55 (1987), 879888. MR 916125 (89a:42029)
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 A. Wald, Sequential analysis, Wiley, New York, 1974. MR 0020764 (8:593h)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029939199311310383
PII:
S 00029939(1993)11310383
Article copyright:
© Copyright 1993
American Mathematical Society
