Restricted weak-type Rubio de Francia extrapolation for p > p0 with applications to exponential integrability estimates

Given Aˆp, the class of weights w of the form w=(Mg)1−pu for some g∈Lloc1(Rn) and u∈A1, the following result is proved: Let p0>1 and let T be an operator such that, for every v∈Aˆp0,T:Lp0,1(v)⟶Lp0,∞(v) is bounded, with constant less than or equal to φ(‖v‖Aˆp0). Then, for every p>p0 and every v∈Aˆp,T:Lp,1(v)⟶Lp,∞(v) is bounded with a precise control of the constant depending on ‖v‖Aˆp and φ. As a consequence, exponential integrability estimates are proved for several classes of operators appearing in Harmonic Analysis. This paper is a continuation of [3], where the restricted weak-type extrapolation for p