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Some properties of analytic functions on the unit ball with hadamard gaps

In this paper, we describe some criteria for an analytic function f on the unit ball B, with Hadamard gaps, to belong to the Besov space X p and the space B p, respectively. The special case of the space B p is BMOA. We use these results, together with Ryll-Wojtaszczyk polynomials, to show that the following containments and are proper.