  We apply the leading-log high-energy resummation technique recently derived
by some of us to the transverse momentum (pt) distribution for production of a
Higgs boson in gluon fusion. We use our results to obtain information on
mass-dependent corrections to this observable, which is only known at leading
order when exact mass dependence is included. In the low pt region we discuss
the all-order exponentiation of collinear bottom mass logarithms. In the high
pt region we show that the infinite top mass approximation loses accuracy as a
power of pt, while the accuracy of the high-energy approximation is
approximately constant as pt grows. We argue that a good approximation to the
NLO result for pt >~200 GeV can be obtained by combining the full LO result
with a K-factor computed using the high-energy approximation.
