Area integral functions and $H^{\text{8}}$ functional calculus for sectorial operators on Hilbert spaces

Area integral functions are introduced for sectorial operators on Hilbert spaces. We establish the equivalence relationship between the square and area integral functions. This immediately extends McIntosh/Yagi’s results on $H^{\text{8}}$ functional calculus of sectorial operators on Hilbert spaces to the case when the square functions are replaced by the area integral functions.