Weighted inequalities for fractional integral operators with kernel satisfying H\"ormander type conditions

ANA L. BERNARDIS; MARÍA LORENTE; MARÍA SILVINA RIVEROS

MATHEMATICAL INEQUALITIES & APPLICATIONS

ELEMENT

Año: 2011 vol. 14 p. 881 - 895

1331-4343

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 H"ormander 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.