Bloch functions on the unit ball of a Banach space
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Title
Bloch functions on the unit ball of a Banach spaceAuthor (s)
Date
2021-02-10Publisher
American Mathematical SocietyISSN
1088-6826; 0002-9939Bibliographic citation
Miralles, A. (2021). Bloch functions on the unit ball of a Banach space. Proceedings of the American Mathematical Society, 149(4), 1459-1470.Type
info:eu-repo/semantics/articleVersion
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Abstract
The space of Bloch functions on bounded symmetric domains is extended by considering Bloch functions f on the unit ball BE of nite and in nite dimensional complex Banach spaces in two di erent ways: by extending the ... [+]
The space of Bloch functions on bounded symmetric domains is extended by considering Bloch functions f on the unit ball BE of nite and in nite dimensional complex Banach spaces in two di erent 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 that all bounded analytic functions on BE are Bloch functions in both ways. [-]
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Proceedings of the American Mathematical Society, 149 (2021)Project code
PGC2018-094431-B-100 | GV/2018/110
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