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Differentiation in Star-Invariant Subspaces I. Boundedness and Compactness

✍ Scribed by Konstantin M. Dyakonov


Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
199 KB
Volume
192
Category
Article
ISSN
0022-1236

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Differentiation in Star-Invariant Subspa
✍ Konstantin M. Dyakonov πŸ“‚ Article πŸ“… 2002 πŸ› Elsevier Science 🌐 English βš– 201 KB

Given an inner function y on the upper half-plane C ΓΎ , let K y :ΒΌ H 2 Γ‰ yH 2 be the corresponding star-invariant subspace of the Hardy space H 2 . Earlier we showed that the differentiation operator d dx : K y ! L 2 Γ°RÞ is bounded iff y 0 2 L 1 Γ°RÞ and compact iff y 0 2 C 0 Γ°RÞ. The current problem