Bloch space  In the mathematical field of complex analysis, the Bloch space, named after French mathematician André Bloch and denoted formula_1 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. formula_1 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.