Bloch space explained

In the mathematical field of complex analysis, the Bloch space, named after French mathematician André Bloch and denoted

l{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.

l{B} is a type of Banach space, with the norm defined by\|f\| _{l{B}=} |f( 0 )| + \sup _{z} ( 1- |z| ^{2)} |f'(z)|.

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