  We construct two bounded functional calculi for sectorial operators on Banach
spaces, which enhance the functional calculus for analytic Besov functions, by
extending the class of functions, generalizing and sharpening estimates, and
adapting the calculus to the angle of sectoriality. The calculi are based on
appropriate reproducing formulas, they are compatible with standard functional
calculi and they admit appropriate convergence lemmas and spectral mapping
theorems. To achieve this, we develop the theory of associated function spaces
in ways which are interesting and significant. As consequences of our calculi,
we derive several well-known operator norm-estimates and provide
generalizations of some of them.
