WEIGHTED INTEGRAL-INEQUALITIES FOR THE HARDY TYPE OPERATOR AND THE FRACTIONAL MAXIMAL OPERATOR

Let w(x), u(x) and v(x) be weight functions. In this paper, under appr opriate conditions on Young's functions PHI1, PHI2 we characterize the inequality PHI2(-1)(integral-infinity/0 PHI2(Tf(x))w(x)dx) less-than- or-equal-to PHI1(-1)(integral-infinity/0 PHI1(Cf(x)u(x))v(x)dx) for th e Hardy-type operator T defined in [1] and the inequality PHI2-1(integ ral(Rn) PHI2(M(alpha,nu)(fv)(x))w(x)dv(x)) less-than-or-equal-to PHI1( -1) (integral(Rn) PHI1(Cf(x))v(x)dv(x)) for the fractional maximal ope rator M(alpha,v) defined in [8], as well as the corresponding weak-typ e inequalities.