Abstract
For 12<p<∞, 0 < q< ∞ and a certain two-sided doubling weight ω, we characterize those inner functions Θ for which ‖Θ′‖Aωp,qq=∫01(∫02π|Θ′(reiθ)|pdθ)q/pω(r)dr<∞.Then we show a modified version of this result for p⩾ q. Moreover, two additional characterizations for inner functions whose derivative belongs to the Bergman space Aωp,p are given.
| Original language | English |
|---|---|
| Pages (from-to) | 1853-1871 |
| Number of pages | 19 |
| Journal | Complex Analysis and Operator Theory |
| Volume | 13 |
| Issue number | 4 |
| DOIs | |
| Publication status | Published - 2019 Jun 1 |
Keywords
- Bergman space
- Blaschke product
- Frostman shift
- Hardy space
- Inner function
- Mixed norm space