论文标题
多变量$ h^\ infty $功能计算的新属性
New properties of the multivariable $H^\infty$ functional calculus of sectorial operators
论文作者
论文摘要
本文致力于与有限的班克空间上的有限通勤家族相关的多变量$ h^\ infty $函数演算。 First we prove that if $(A_1,\ldots, A_d)$ is such a family, if $A_k$ is $R$-sectorial of $R$-type $ω_k\in(0,π)$, $k=1,\ldots,d$, and if $(A_1,\ldots, A_d)$ admits a bounded $ h^\ infty（σ_{θ_1} \ times \ cdots \timesς_{θ_d}）$ in（ω_k，π）$的某些$θ_k\ in（ω_k，π）$的关节功能计算，然后它接纳一个有界的$ h^\ inty $ h^\ infty（所有$θ_k\ in（ω_k，π）$，$ k = 1，\ ldots，d $的功能计算。其次，我们引入了适合多变量情况的正方形函数，并扩展到此设置的一些众所周知的单变量结果，将$ H^\ infty $ functional colkulus与Square函数估计的界限有关。第三，在$ k $ -convex的反射空间上，我们建立了$ d $ - tuples $（a_1，\ ldots，a_d）$的急剧扩张属性，该$接纳了有限的$ h^\ infty（σ_{θ_1} \ times \ times \ cdots \ cdots \ cdots \ cd \ times \ times \ timesdiminitialitional functions $ intimitiational fuckitions formitional collectional collectional collectional callus in $θ_K<\fracπ{2} $。
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 $ω_k\in(0,π)$, $k=1,\ldots,d$, and if $(A_1,\ldots, A_d)$ admits a bounded $H^\infty(Σ_{θ_1}\times \cdots\timesΣ_{θ_d})$ joint functional calculus for some $θ_k\in (ω_k,π)$, then it admits a bounded $H^\infty(Σ_{θ_1}\times \cdots\timesΣ_{θ_d})$ joint functional calculus for all $θ_k\in (ω_k,π)$, $k=1,\ldots,d$. 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 $H^\infty(Σ_{θ_1}\times \cdots\timesΣ_{θ_d})$ joint functional calculus for some $θ_k<\fracπ{2}$.
