Bloch space

Template:Short description In the mathematical field of complex analysis, the Bloch space, named after French mathematician 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

$(1-|z{|}^2)|f^{\prime }(z)|$

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

$\Vert f{\Vert }_{ℬ}=|f(0)|+\underset{z\in 𝐃}{\sup }(1-|z{|}^2)|f^{\prime }(z)|.$

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

Notes

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