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Published online by Cambridge University Press: 22 January 2016
Note that an extra condition of symmetry of f, namely, the boundedness of f(x) = f(− x) is added to the hypothesis of the Lemma. Lemma 2.1 was used in three places in the paper to prove that the functions F, G*, and f given in pages 140, 141, and 144, respectively, belong to BMO. It can be checked by a standard argument that these functions satisfy the symmetry condition.