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Journal article
Derivatives of rational inner functions: geometry of singularities and integrability at the boundary
Proceedings of the London Mathematical Society, v 116(2), pp 281-329
Feb 2018
Abstract
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 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.
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Details
- Title
- Derivatives of rational inner functions: geometry of singularities and integrability at the boundary
- Creators
- Kelly Bickel - Bucknell UniversityJames Eldred Pascoe - Washington University in St. LouisAlan Sola - Stockholm University
- Publication Details
- Proceedings of the London Mathematical Society, v 116(2), pp 281-329
- Publisher
- Wiley
- Number of pages
- 49
- Grant note
- 1448846 / National Science Foundation DMS; National Science Foundation (NSF) 1606260 / National Science Foundation Postdoctoral Fellowship DMS
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Mathematics
- Web of Science ID
- WOS:000424388300003
- Scopus ID
- 2-s2.0-85028645236
- Other Identifier
- 991021879782804721
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- Collaboration types
- Domestic collaboration
- International collaboration
- Web of Science research areas
- Mathematics