Weak weighted inequalities for a dyadic one-sided maximal function in Rn

In this note we introduce a dyadic one-sided maximal function defined as M(+,d)f( x) = sup(Qdyadic:x is an element of Q)1|Q|integral(Q+)|f|, where Q(+) is a certain cube associated with the dyadic cube Q and f is an element of L-loc(1) (R-n). We characterize the pair of weights ( w, v) for which the maximal operator M-+,M-d applies L-p (v) into weak-L-p (w) for 1 <= p < infinity.