A characterization of weights u, v is given for which the geometric me
an operator Tf(x) = exp(1/x integral-x/0 fox In f(t) dt) , defined for
f positive a.e. on (0, infinity) , is bounded from L(p)((0, infinity)
; v dx) to L(q)((0, infinity); u dx), p is-an-element-of (0, infinity)
and q is-an-element-of [p, infinity).