Bloch space

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

$(1-|z|^2)|f^\prime(z)|$

is bounded. $\mathcal{B}$ is a Banach space, with the norm defined by

$\|f\|_\mathcal{B} = |f(0)| + \sup_{z \in \mathbf{D}} (1-|z|^2) |f'(z)|.$

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