A New Class of Weights Adapted to Rough Singular Integrals and Marcinkiewicz Integrals

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