No abstract

No abstract

We use an appropriate factorization of the A p weights to give another proof of the extrapolation theorem of Rubio de Francia. It provides sharp bounds in terms of the A p -constant of the weights. Then we extend the result to more general settings including off-diagonal and partial range extrapolation. Among the applications, we prove by iteration a multivariable extrapolation theorem and give a sharp bound for Calderón-Zygmund operators on L p (w) for weights in A q (q < p).

Abstract. We prove weighted norm inequalities for homogeneous singular integrals when only a size condition is assumed on the restriction of the kernel to the unit sphere. The same results hold for the operator obtained by modifying the centered Hardy-Littlewood maximal operator over balls with a degree zero homogeneous function and also for the maximal singular integral.

No abstract