Weighted inequalities for fractional integral operators with kernel satisfying Hörmander type conditions

Abstract

In this paper we study inequalities with weights for fractional operators Tαgiven by convolution with a kernel Kαwhich is supposed to satisfy some size condition and a fractional Hörmander type condition. As it is done for singular integrals, the conditions on the kernel have been generalized from the scale of Lebesgue spaces to that of Orlicz spaces. Our fractional operators include as particular cases the classical fractional integral Iα, fractional integrals associated to an homogeneous function and fractional integrals given by a Fourier multiplier.