论文标题
理性的内部功能及其Dirichlet类型规范
Rational inner functions and their Dirichlet type norms
论文作者
论文摘要
我们研究了多迪斯克中迪奇特型空间中有理内部功能的成员资格。特别是，我们证明了一种定理，将这种包含物与$ h^p $相关的RIF的部分衍生物的可集成性有关，作为推论，我们证明所有理性的内部功能都属于$ \ mathbb {d}^n $属于$ \ natercal {D}此外，我们表明，如果$ 1/p \ in \ Mathcal {d} _ {α，...，...，α} $，则RIF $ \ tilde {p}/p \ in \ int \ atmatcal {d} _ {d} _ {α+2/n，...，α+2/n} $。最后，我们说明了如何通过几个示例应用这些结果，以及如何应用Lojasiewicz不等式来确定在某些dirichlet型空间中包含$ 1/p $。
We study membership of rational inner functions in Dirichlet-type spaces in polydisks. In particular, we prove a theorem relating such inclusions to $H^p$ integrability of partial derivatives of a RIF, and as a corollary we prove that all rational inner functions on $\mathbb{D}^n$ belong to $\mathcal{D}_{1/n, \ldots ,1/n}(\mathbb{D}^n)$. Furthermore, we show that if $1/p \in \mathcal{D}_{α,...,α}$, then the RIF $\tilde{p}/p \in \mathcal{D}_{α+2/n,...,α+2/n}$. Finally we illustrate how these results can be applied through several examples, and how the Lojasiewicz inequality can sometimes be applied to determine inclusion of $1/p$ in certain Dirichlet-type spaces.
