# What is the term used for space of analytic functions?

I deal with analytic functions in the unit disc represented as the series $\sum_{n=0}^\infty u_n z^n$, where the coefficients $u_n$ satisfy the condition $\sum_{n=0}^\infty n^\alpha|u_n| < \infty$ with $\alpha > 0$.

Does there exist any commonly used name for the spaces of such functions?

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