Bloch space

In the mathematical field of complex analysis, the Bloch space, named after 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

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

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