Bloch functions on the unit ball of a Banach space

2018/02/22 by Miralles, Alejandro
#FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1802.08098

Abstract

The space of Bloch functions on bounded symmetric domains is extended by considering Bloch functions f on the unit ball B_E of finite and infinite dimensional complex Banach spaces in two different ways: by extending the classical Bloch space considering the boundness of (1-‖x‖²) ‖f'(x)‖ on B_E and by preserving the invariance of the correspondiing seminorm when we compose with automorphisms ϕ of B_E. We study the connection between these spaces proving that they are different in general and prove that all bounded analytic functions on B_E are Bloch functions in both ways.

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