A new class of weights adapted to rough singular integrals and Marcinkiewicz integrals

In this paper, we introduce a new class of weights A.p(Rn) which retains many fine properties of the classical Muchenhoupt weights A p (.n). While A p (.n) is too big a class to obtain the weighted norm inequalities for rough singular integrals and Marcinkiewicz integrals, our new class A.p(Rn) adapts well to these rough operators. As applications, we improve some known weighted estimates.