✦ LIBER ✦
Embedding Theorems for Star-Invariant Subspaces Generated by Smooth Inner Functions
✍ Scribed by Konstantin M. Dyakonov
- Publisher
- Elsevier Science
- Year
- 1998
- Tongue
- English
- Weight
- 244 KB
- Volume
- 157
- Category
- Article
- ISSN
- 0022-1236
No coin nor oath required. For personal study only.
✦ Synopsis
Given an inner function % on the unit disk D, let K p % :=H p & %zÄ H p be the corresponding star-invariant subspace of the Hardy space H p . We are concerned with embedding theorems of the form K p % /L q (+), where + is a measure on D, and some related norm inequalities. In particular, assuming that % has a certain smoothness property, we characterize the +'s such that every f # K 1 % satisfies
where 1 q< and 0<:<1. This result sheds some light on the nature of Carleson-type measures for K p % .
1998 Academic Press K 2 % /L 2 (+).
(1.2) (Here and throughout, a measure'' means a positive Borel measure''.