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 $\beta \in (0,1]$.

  • $\begingroup$ Where have you found this notation? $\endgroup$ Commented Jan 7, 2016 at 14:51
  • 3
    $\begingroup$ Without context it's hard to know for sure, but i'm guessing Hölder continuous functions of exponent $\beta$. $\endgroup$
    – mrf
    Commented Jan 7, 2016 at 14:53


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