EXTENSIONS OF RUBIO DE FRANCIA'S EXTRAPOLATION THEOREM

摘要: One of the main results in modern harmonic analysis is extrapolation theorem J.L. Rubio de Francia for Ap weights. In this paper we discuss some recent extensions this result. We present a new approach that, among other things, allows us to obtain estimates in rearrangement-invariant Banach function spaces as well as weighted modular inequalities. also extend extrapolation technique to context A1 apply obtained dyadic square function. Fractional integrals, singular integral operators and their commutators with bounded mean oscillation functions are considered. present an extension classical of Boyd and Lorentz-Shimogaki a wider class operators to weighted vector-valued estimates. Finally, same kind ideas leads extrapolate within appropriate of non weights can be used prove conjecture proposed by E. Sawyer.