Holder and locally Holder continuous functions. The linear …
https://link.springer.com/content/pdf/10.1007/978-3-319-47940-8_1.pdf
WEBset, it is uniformly continuous; nally, it is also absolutely continuous. Proof. Assume, on the contrary, that fis -H older continuous. For x;y2[0;1=2] inequality (1.5), p.4holds, and therefore, in particular, since f(0) = 0, jf(x)j [f] x ; 8x2]0; 1 2]; i.e., 1 x jlogxj [f] ; 8x2]0; 1 2]: This is absurd, since the left-hand side diverges as x!0.
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