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

TL;DR

This paper introduces area integral functions for sectorial operators on Hilbert spaces and proves their equivalence with square functions, extending existing $H^{\

Contribution

It extends the $H^{\8}$ functional calculus for sectorial operators by replacing square functions with area integral functions, broadening the analytical tools available.

Findings

Established equivalence between square and area integral functions

Extended McIntosh/Yagi's $H^{\8}$ calculus results to area integral functions

Provided new methods for analyzing sectorial operators on Hilbert spaces

Abstract

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 $H^{\8}$ functional calculus of sectorial operators on Hilbert spaces to the case when the square functions are replaced by the area integral functions.