# Bloch space

In the mathematical field of complex analysis, the Bloch space, named after André Bloch and denoted ${\displaystyle {\mathcal {B}}}$ 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
${\displaystyle (1-|z|^{2})|f^{\prime }(z)|}$
is bounded.[1] ${\displaystyle {\mathcal {B}}}$ is a Banach space, with the norm defined by
${\displaystyle \|f\|_{\mathcal {B}}=|f(0)|+\sup _{z\in \mathbf {D} }(1-|z|^{2})|f'(z)|.}$