Let Θ be an inner function and let α ∈ ℂ, |α| = 1. Denote by σα the nonnegative singular measure whose Poisson integral is equal to Re α+Θ/α-Θ. A theorem of Clark provides a natural unitary operator Uα that identifies H2 ⊖ ΘH2 with L 2(σα). The following fact is established. Assume that f ∈ H2 ⊖ ΘH2, 2 < p ≤ + ∞, α ≠ β. Then ∥f∥Hp ≤ C(α,β,p)(∥Uα f∥Lp(σα) + ∥Uβf∥Lp(σβ)).
Original language | English |
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Pages (from-to) | 1767-1772 |
Number of pages | 6 |
Journal | Journal of Mathematical Sciences |
Volume | 85 |
Issue number | 2 |
DOIs | |
State | Published - 1997 |
Externally published | Yes |
ID: 87313016