Holder spaces. https://math.ucdenver.edu/~jmandel/classes/7760f05/spaces.pd...
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Let Ω be an open set in Rn, 0<α≤1, and k a nonnegative integer. The (uniform) Holder spaces Ck,α(Ω) consist of functions whose k−th order derivatives are uniformly Holder continuous with exponent α in Ω. The(local) Holder spaces Ck,α(Ω) consist of functions whose k−th order derivatives are locally Holder continuous with exponent α
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The Holder continuity condition looks sorta like the limit definition of a derivative with an exponent on the denominator.