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Representations for the Bloch type semi-norm of Fréchet differentiable mappings. (English) Zbl 1477.32004

Summary: In this paper we give some results concerning Fréchet differentiable mappings between domains in normed spaces with controlled growth. The results are mainly motivated by Pavlović’s equality for the Bloch semi-norm of continuously differentiable mappings in the Bloch class on the unit ball of the Euclidean space as well as the very recent Jocić’s generalization of this result.

MSC:

32A18 Bloch functions, normal functions of several complex variables
32A37 Other spaces of holomorphic functions of several complex variables (e.g., bounded mean oscillation (BMOA), vanishing mean oscillation (VMOA))
46G05 Derivatives of functions in infinite-dimensional spaces
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References:

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