论文标题
通勤的RITT运营商家庭的平方功能
Square functions for commuting families of Ritt operators
论文作者
论文摘要
在本文中，我们调查了针对通勤RITT操作员$（T_1，...，...，T_D）$的正方形功能的作用，该函数在一般的Banach Space $ x $上作用。首先，我们证明，如果$ d $ tuple允许$ h^\ infty $ intim $联合功能计算，那么它将验证各种平方函数估计。然后，当每个$ t_k $都是$ r $ -RITT操作员时，我们研究相反的情况。在最后一个假设下，当$ x $是$ k $ -convex空间时，我们表明，在某些bochner space $ l_p（ω; x）$ $ d $ d $ - iSomorphisms中，方函数估计了$（t_1，...，...，t_d）$的产量扩张为$（t_1，...，t_d）$。最后，我们比较了RITT运营商的$ h^\ infty $联合功能积分的$ d $ tuple，其扩张为多项式限制的同构。
In this paper, we investigate the role of square functions defined for a $d$-tuple of commuting Ritt operators $(T_1,...,T_d)$ acting on a general Banach space $X$. Firstly, we prove that if the $d$-tuple admits a $H^\infty$ joint functional calculus, then it verifies various square function estimates. Then we study the converse when every $T_k$ is a $R$-Ritt operator. Under this last hypothesis, and when $X$ is a $K$-convex space, we show that square function estimates yield dilation of $(T_1,...,T_d)$ on some Bochner space $L_p(Ω;X)$ into a $d$-tuple of isomorphisms with a $C(\mathbb{T}^d)$ bounded calculus. Finally, we compare for a $d$-tuple of Ritt operators its $H^\infty$ joint functional calculus with its dilation into a $d$-tuple of polynomially bounded isomorphisms.
