Factorization of derivatives of Bloch mappings through a Hilbert space

M. G. Cabrera-PadillaA. Jim\'enez-VargasD. Ruiz-Casternado

Nov 2023

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We introduce the concept of vector-valued holomorphic mapping on the complex unit disc whose derivative factors through a Hilbert space and state the main properties of the space formed by such Bloch mappings equipped with a natural norm: linearization, Bloch transposition, surjective and injective Banach ideal property, invariance by M\"obius transformations, Kwapi\'en-type characterization by Bloch domination, and duality.

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