Bloch space

In the mathematical field of complex analysis, the Bloch space, named after French mathematician 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 type of 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.