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- W3041416357 abstract "This paper is devoted to the multivariable $H^infty$ functional calculus associated with a finite commuting family of sectorial operators on Banach space. First we prove that if $(A_1,ldots, A_d)$ is such a family, if $A_k$ is $R$-sectorial of $R$-type $omega_kin(0,pi)$, $k=1,ldots,d$, and if $(A_1,ldots, A_d)$ admits a bounded $H^infty(Sigma_{theta_1}times cdotstimesSigma_{theta_d})$ joint functional calculus for some $theta_kin (omega_k,pi)$, then it admits a bounded $H^infty(Sigma_{theta_1}times cdotstimesSigma_{theta_d})$ joint functional calculus for all $theta_kin (omega_k,pi)$, $k=1,ldots,d$. Second we introduce square functions adapted to the multivariable case and extend to this setting some of the well-known one-variable results relating the boundedness of $H^infty$ functional calculus to square function estimates. Third, on $K$-convex reflexive spaces, we establish sharp dilation properties for $d$-tuples $(A_1,ldots, A_d)$ which admit a bounded $H^infty(Sigma_{theta_1}times cdotstimesSigma_{theta_d})$ joint functional calculus for some $theta_k<frac{pi}{2}$." @default.
- W3041416357 created "2020-07-16" @default.
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- W3041416357 date "2020-07-09" @default.
- W3041416357 modified "2023-09-27" @default.
- W3041416357 title "New properties of the multivariable $H^infty$ functional calculus of sectorial operators" @default.
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