Characterization of lacunary functions in weighted Bergman–Besov–Lipschitz spaces

Abstract

We consider the weighted Bergman–Besov–Lipschitz space B ρ of analytic functions F in the unit disc 𝔻 = {z ∈ ℂ, |z| ≤ 1} for which and we show that a lacunary function belongs to B ρ if and only if the sequence a n satisfies , where I n are diadic intervals defined by I n = {k ∈ ℕ : 2 n−1 ≤ k < 2 n }, ρ belongs to a certain class of weights and K(n, ρ) > 0 is a function of n and ρ.