U+212C Script Capital B

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

$(1-|z{|}^2)|f^{\prime }\left(z\right)|$

is bounded. $B$ is a type of Banach space, with the norm defined by

$\Vert f{\Vert }_B=|f\left(0\right)|+\underset{z\in D}{sup}(1-|z{|}^2)|f^{\prime }\left(z\right)|.$

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