Two Weight Extrapolation via the Maximal Operator

By D. Cruz-Uribe, C. P'erez. 2000

68 citations recorded by the source corpus.

Abstract We give several extrapolation theorems for pairs of weights of the form ( w , M k w ) and ( w , ( Mw / w ) r w ), where w is any non-negative function, r >1, and M k is the k th 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.

Subfields: Applied Mathematics

View Paper: https://www.semanticscholar.org/paper/97343337825cefa92629dec926067cb3d41bc3a7

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

Citations in the corpus

Weighted Norm Inequalities for the Local Sharp Maximal Function (2004, background): “Several important applications of this theorem to square functions and singular integrals are given in [4].”
Sharp weighted estimates for classical operators (2010, background): “The example in [9] shows that if A(t) = t log(e+t), then the result fails if δ = 0, when A 6∈ B(p/q)′ .”
Sharp weighted estimates for vector-valued singular integral operators and commutators (2003, methodology): “11) improves the result obtained for [h, T ]q as an application of the general extrapolation theorem from [5] derived from the scalar estimate given in [14, Theorem 2].”
On Muckenhoupt–Wheeden Conjecture☆ (2010, background): “The dyadic version of this result is also true (see [5], Remark 1.”