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Let ψ be a non-decreasing continuous subadditive function defined on [0, ∞) and satisfy ψ(x) = 0 if and only if x = 0. The space H(ψ) is defined as the set of analytic functions in the unit disk which satisfy
and the space H+ (ψ) is the space of a f ∊ H(ψ) for which
where 
almost everywhere.
In this paper we study the H(ψ) spaces and characterize the continuous linear functionals on H+ (ψ).
