# What does notation $C^{\beta}[0,1]$ mean?

What does the notation $C^{\beta}[0,1]$ for $\beta \in (0,1]$ mean? I know $C[0,1]$ is the space of all continuous functions on the interval $[0,1]$, but what about $C^{\beta}[0,1]$? Usually $C^k[0,1]$ is the space of functions with $k$-th continuous derivative, but now $\beta \in (0,1]$.

• Where have you found this notation? – Henning Makholm Jan 7 '16 at 14:51
• Without context it's hard to know for sure, but i'm guessing Hölder continuous functions of exponent $\beta$. – mrf Jan 7 '16 at 14:53