Journal of Operator Theory

Volume 49, Issue 1, Winter 2003 pp. 85-97.

More relative angular derivatives

Authors: Jonathan E. Shapiro
Author institution: Department of Mathematics, California Polytechnic State University, San Luis Obispo, CA 93407, Obispo, CA 93407, USA

Summary: The notion of the angular derivative of a holomorphic self-map $b$ of the unit disk has been generalized to that of an angular derivative of $b$ relative to an inner function $u$.\ In this paper, we provide three more conditions equivalent to the existence of an angular derivative of $b$ relative to $u$, and use these notions to provide a generalization of Julia's lemma.

Keywords: angular derivative, Hardy space, Aleksandrov measure

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