Let Θ be an inner function and let α ∈ ℂ, |α| = 1. Denote by σ_α the nonnegative singular measure whose Poisson integral is equal to Re α+Θ/α-Θ. A theorem of Clark provides a natural unitary operator U_α that identifies H² ⊖ ΘH² with L ²(σ_α). The following fact is established. Assume that f ∈ H² ⊖ ΘH², 2 < p ≤ + ∞, α ≠ β. Then ∥f∥_Hp ≤ C(α,β,p)(∥U_α f∥_Lp(σα) + ∥U_βf∥_Lp(σβ)).