Extrapolation from A∞ weights and applications
|Author||Cruz Uribe, David
Martell Berrocal, José María
Pérez Moreno, Carlos
|Department||Universidad de Sevilla. Departamento de Análisis Matemático|
|Abstract||We generalize the Ap 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 ...
We generalize the Ap 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 Lp 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 Calder´on-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.
|Funding agencies||Ministerio de Ciencia y Tecnología (MCYT). España|
|Citation||Cruz Uribe, D., Martell Berrocal, J.M. y Pérez Moreno, C. (2004). Extrapolation from A∞ weights and applications. Journal of Functional Analysis, 213 (2), 412-439.|