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{c}
{title2=$[f]_{C^{0,\alpha}}$}

The Hölder seminorm of exponent $0<\alpha\leq1$ is
$$
[f]_{C^{0,\alpha}}=\sup_{x\ne y}\frac{|f(x)-f(y)|}{|x-y|^\alpha}.
$$
It measures <Hölder continuity> without including the <supremum norm> of the function itself.

Hölder seminorm

Past exam of the mathematics course of the University of Cambridge / 2018 / ii / Paper 4 / 23F / b / Solution

Hölder seminorm ( $[f]_{C^{0, α}}$ )

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Hölder seminorm ([f]C0,α​)

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Hölder seminorm ( $[f]_{C^{0, α}}$ )

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