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Proceedings of the American Mathematical Society

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Bourgain’s analytic projection revisited

Author: S. V. Kislyakov
Journal: Proc. Amer. Math. Soc. 126 (1998), 3307-3314
MSC (1991): Primary 30D55, 46E15
MathSciNet review: 1458882
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Abstract: For a positive function $w$ on the unit circle with $\log w\in L^1$, the following two statements are equivalent: (a) $\log w\in BMO$; (b) there is an operator $Q$ projecting $L^p(w)$ onto $H^p(w)$ for all $1<p<\infty$ at once and having weak type (1,1) with respect to $w$.

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S. V. Kislyakov
Affiliation: Université Bordeaux I, Laboratoire de Mathématiques Pures, 351 cours de la Libération, F-33405 Talence Cedex 05, France; Steklov Mathematical Institute, St. Petersburg Branch, Fontanka 27, 191011 St. Petersburg, Russia

Keywords: Weight, analytic decomposition of unity, analytic projection, $BMO$-regular space
Received by editor(s): March 30, 1997
Communicated by: Theodore W. Gamelin
Article copyright: © Copyright 1998 American Mathematical Society