  We develop a very general operator-valued functional calculus for operators
with an $H^{\infty}-$calculus. We then apply this to the joint functional
calculus of two commuting sectorial operators when one has an
$H^{\infty}$calculus. Using this we prove theorem of Dore-Venni type on sums of
commuting sectorial operators and apply our results to the problem of
$L_p-$maximal regularity. Our main assumption is the R-boundedness of certain
sets of operators, and therefore methods from the geometry of Banach spaces are
essential here. In the final section we exploit the special Banach space
structure of $L_1-$spaces and $C(K)-$spaces, to obtain some more detailed
results in this setting.
