A REMARK ON SINGULAR-INTEGRALS AND POWER WEIGHTS

In this work we present several general theorems which imply the boundedness on weighted Lorentz spaces L(p)(\x\(alpha)dx) for sublinear operators T, which are known to be bounded in the unweighted case alpha = 0, under certain weak conditions on the size of T. Applications are given to singular integrals and vector valued operators. In particular we recover (and extend) some recents results by S. Hofmann on rough maximal and singular operators.