A NOTE ON WEIGHTED INEQUALITIES FOR A ONE-SIDED MAXIMAL OPERATOR IN Rn

We introduce a new dyadic one-sided maximal operator M-d(+...+) in R-n that allows us to obtain good weights for the L-p-boundedness of a one-sided maximal operator N+...+ in R-n, which is equivalent to the classical one-sided Hardy-Littlewood maximal operator in the case n = 1, but not in the case n > 1. In order to do this, we characterize the good pairs of weights for the weak and strong type inequalities for M-d(+...+) and we use a Fefferman Stein type inequality which gives that, in a certain sense, M-d(+...+) controls N+...+.