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In the mathematical field of complex analysis, the **Bloch space**, named after French mathematician André Bloch and denoted 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.^{[1]} is a type of 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**.

**^**Wiegerinck, J. (2001) [1994], "Bloch function",*Encyclopedia of Mathematics*, EMS Press