WEIGHTED INEQUALITIES FOR FRACTIONAL INTEGRAL OPERATORS WITH KERNEL SATISFYING HORMANDER TYPE CONDITIONS

In this paper we study inequalities with weights for fractional operators T-alpha given by convolution with a kernel K-alpha which is supposed to satisfy some size condition and a fractional Hormander 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 I-alpha, fractional integrals associated to an homogeneous function and fractional integrals given by a Fourier multiplier.