Bloch space

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In the mathematical field of complex analysis, the Bloch space, named after André Bloch and denoted or ℬ, is the space of holomorphic functions f defined on the open unit disc D in the complex plane, such that the function

is bounded.[1] is a Banach space, with the norm defined by

This is referred to as the Bloch norm and the elements of the Bloch space are called Bloch functions.

Notes[edit]

  1. ^ Wiegerinck, J. (2001) [1994], "Bloch function", in Hazewinkel, Michiel, Encyclopedia of Mathematics, Springer Science+Business Media B.V. / Kluwer Academic Publishers, ISBN 978-1-55608-010-4