Bloch functions on the unit ball of a Banach space

Alejandro Miralles
2019 Proceedings of the American Mathematical Society  
The space of Bloch functions on bounded symmetric domains is extended by considering Bloch functions f on the unit ball BE 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 BE and by preserving the invariance of the correspondiing seminorm when we compose with automorphisms ϕ of BE. We study the connection between these spaces proving that they are different in general and prove
more » ... hat all bounded analytic functions on BE are Bloch functions in both ways. 2010 Mathematics Subject Classification. Primary 30D45, 46E50. Secondary 46G20.
doi:10.1090/proc/14966 fatcat:77yj4yl2uvehpegilrbatsupoa