Extrapolation from A ∞ weights and applications

73Citations
Citations of this article
7Readers
Mendeley users who have this article in their library.

Abstract

We generalize the A p extrapolation theorem of Rubio de Francia to A ∞ weights in the context of Muckenhoupt bases. Our result has several important features. First, it can be used to prove weak endpoint inequalities starting from strong-type inequalities, something which is impossible using the classical result. Second, it provides an alternative to the technique of good-λ inequalities for proving L p norm inequalities relating operators. Third, it yields vector-valued inequalities without having to use the theory of Banach space valued operators. We give a number of applications to maximal functions, singular integrals, potential operators, commutators, multilinear Calderón-Zygmund operators, and multiparameter fractional integrals. In particular, we give new proofs, which completely avoid the good-λ inequalities, of Coifman's inequality relating singular integrals and the maximal operator, of the Fefferman-Stein inequality relating the maximal operator and the sharp maximal operator, and the Muckenhoupt-Wheeden inequality relating the fractional integral operator and the fractional maximal operator. © 2003 Elsevier Inc. All rights reserved.

Cite

CITATION STYLE

APA

Cruz-Uribe, D., Martell, J. M., & Pérez, C. (2004). Extrapolation from A ∞ weights and applications. Journal of Functional Analysis, 213(2), 412–439. https://doi.org/10.1016/j.jfa.2003.09.002

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Save time finding and organizing research with Mendeley

Sign up for free