Derivatives of rational inner functions: geometry of singularities and integrability at the boundary
Derivatives of rational inner functions: geometry of singularities and integrability at the boundary
复制标题
有理内函数的导数：奇点几何和边界可积
DOI：
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发表时间：
2017
期刊：
影响因子：
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通讯作者：
A. Sola
中科院分区：
文献类型：
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作者：
K. Bickel;J. Pascoe;A. Sola
我们分析了单位双圆盘上有理内函数的奇异性，并研究了这些函数何时属于Dirichlet-型空间以及它们的偏导数何时属于哈代空间.我们的特点是衍生Hp成员纯粹的接触顺序，一个RIF的零集接近的bidisk的杰出的边界的速率的措施。我们还证明了具有奇异性的RIF的导数对于p ≠ 32不能在Hp中，并且RIF的更高的非切向正则性矛盾地降低了其导数的Hp可积性。我们从Hp的导数包含导出Dirichlet-型空间的包含结果。利用Agler分解和局部Dirichlet积分，我们进一步证明了一类限制性的RIF不属于未加权Dirichlet空间。
We analyze the singularities of rational inner functions (RIFs) on the unit bidisk and study both when these functions belong to Dirichlet‐type spaces and when their partial derivatives belong to Hardy spaces. We characterize derivative Hp membership purely in terms of contact order, a measure of the rate at which the zero set of an RIF approaches the distinguished boundary of the bidisk. We also show that derivatives of RIFs with singularities fail to be in Hp for p⩾32 and that higher non‐tangential regularity of an RIF paradoxically reduces the Hp integrability of its derivative. We derive inclusion results for Dirichlet‐type spaces from derivative inclusion for Hp . Using Agler decompositions and local Dirichlet integrals, we further prove that a restricted class of RIFs fails to belong to the unweighted Dirichlet space.
影响因子：
1.4
作者：
J. Agler;John E. McCarthy;N. Young
通讯作者：
J. Agler;John E. McCarthy;N. Young
bidisc 上分析功能的面部行为
影响因子：
0.9
作者：
Agler J
通讯作者：
Agler J