Suppose a function is Hölder continuous with exponent $\alpha_1 >0$. Then, for $0 < \alpha_2 < \alpha_1$, is it true that the Hölder continuity still holds with exponent $\alpha_2$?
Hölder condition for different exponent
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real-analysis
1 Answers
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0What goes wrong if $a > b$? Can we not take the supremum inside the $(\cdot)^{\frac{a}{b}}$? – 2012-08-08