We give necessary and sufficient conditions for Blaschke products with zeros on an a-curve, to belong to a Qp space, in terms only of distribution of the zeros. It comes out that the condition depends on p. As we see the 0-1 law of the non tangential case breaks. Here it is possible that a Blaschke product B belongs to Qp for some but not for all p.
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For a Blaschke product B with zeros in an angular domain having vertex on the unit circle we give a necessary and sufficient condition for the boundary behavior of B, in terms only of the distribution of the zeros. Moreover, we show, with a counterexample, the non-equivalence of two known results of Tanaka, concerning the specific boundary behavior of Blaschke products.
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