For «>2, a hypersurface in the open unit ball B n in £ " is constructed which satisfies the generalized Blaschke condition and is a uniqueness set for all H p (B n ) with />>0. If n>3, the hypersurface can be chosen to have finite area. Subject classification (Amer. Math. Soc. (MOS) 1970): primary 32 A 10.