2014•Proceedings of the American Mathematical SocietyRequires access
Inner functions with derivatives in the weak Hardy space
Joseph A. Cima, Artur Nicolau
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Abstract
It is proved that exponential Blaschke products are the inner functions whose derivative is in the weak Hardy space. As a consequence, it is shown that exponential Blaschke products are Frostman shift invariant. Exponential Blaschke products are described in terms of their logarithmic means and also in terms of the behavior of the derivatives of functions in the corresponding model space.