Regular Article
Two Weight Extrapolation via the Maximal Operator

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Abstract

We give several extrapolation theorems for pairs of weights of the form (wMkw) and (w, (Mw/w)r w), where w is any non-negative function, r>1, and Mk is the kth iterate of the Hardy–Littlewood maximal operator. As an application we show that our results can be used to extend and sharpen results for square functions and singular integral operators by Chang et al. (1985, Comment. Math. Helv.60, 217–246), Chanillo and Wheeden (1987, Indiana Univ. Math. J.36, 277–294), Wilson (1987, Duke Math. J.55, 879–887; 1989, Trans. Amer. Math. Soc.314, 661–692; 1989, Illinois J. Math.33, 361–366), and Uchiyama (1995, Studia Math.115, 135–149). In the process we prove a conjecture due to Wilson.

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Communicated by Richard, B. Melrose

f1

E-mail: [email protected]

f2

E-mail: [email protected]

1

The second author is partially supported by DGICYT Grant PB940192, Spain.