Английская Википедия:Bloch space

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Шаблон:Short description In the mathematical field of complex analysis, the Bloch space, named after French mathematician André Bloch and denoted <math>\mathcal{B}</math> or ℬ, is the space of holomorphic functions f defined on the open unit disc D in the complex plane, such that the function

<math>(1-|z|^2)|f^\prime(z)|</math>

is bounded.[1] <math>\mathcal{B}</math> is a type of Banach space, with the norm defined by

<math> \|f\|_\mathcal{B} = |f(0)| + \sup_{z \in \mathbf{D}} (1-|z|^2) |f'(z)|. </math>

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

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