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More relative angular derivatives. (English) Zbl 1030.46026
Summary: The notion of 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 notions 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.

46E22 Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces)
46E30 Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)