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The univalent functions in the diagonal Besov space A p , where 1'p'I, are characterized in terms of the distance from the boundary of a point in the image domain. Here A 2 is the Dirichlet space. A consequence is that there exist functions in A p Y p b 2, for which the area of the complement of the image of the unit disc is zero.doi:10.1017/s0017089500010144 fatcat:xher3y66wvcllkhvjrwtr7frkm