2-WEIGHT MIXED PHI-INEQUALITIES FOR THE ONE-SIDED MAXIMAL-FUNCTION

Suppose u, v, w, and t are weight functions on an appropriate measure space (X, mu), and Phi(1), Phi(2) are Young functions satisfying a cer tain relationship. Let T denote an operator to be specified below. The main purpose of this paper is to characterize (i) the strong type mix ed Phi-inequality Phi(2)(-1)(integral(x) Phi(2)(T(fv))w d mu)less than or equal to Phi(1)(-1)(integral(x) Phi(1)(Cf)v d mu), (ii) the weak t ype mixed Phi-inequality Phi(2)(-1)(integral({\Tf\>lambda})Phi(2)(lamb da w)t d mu)less than or equal to Phi(1)(-1)(integral(x) Phi(1)(Cfu)v d mu) and (iii) the extra-weak type mixed Phi-inequality \{x is an ele ment of X:\Tf(x)\ > lambda}\wd mu less than or equal to Phi(2) Phi(1)( -1)(integral(x) Phi(1)(Cfu/lambda)v d mu), when T is the one-sided max imal function M(g)(+); as well to characterize (iii) for the Fefferman -Stein type fractional maximal operator and the Hardy-type operator.