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Finding the solid hull S(H) of the Hardy space H—that is, finding the strongest growth condition the absolute value of the coefficients of H functions must satisfy—is an old and difficult problem. It follows from Littlewood’s theorem on random power series [7, Thm. A.5, p. 228] that S(H) = H 2 for 2 < p < ∞. Much later, Kisliakov [12] identified the solid hull of the space H∞. A deep result of Kisliakov shows that S(H∞) is also H 2. In this paper we identify S(H) in the case 0 < p < 1. The Hardy space H (0 < p ≤ ∞) is the space of all functions f holomorphic in the unit disc U (f ∈H(U)) for which ‖f ‖p = lim r→1p f ) < ∞, where, as usual,

On the solid hull of the Hardy space Hp, 0 < p < 1