Bloch space

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In the mathematical field of complex analysis, the Bloch space, named after André Bloch and denoted or \mathscr{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.