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We can't decuce too much in terms of upper bounds. Note that the inequality is satisfied by the functions $f(x)=cx^{1/2}$, for any constant $c\ge0$ and any nonnegative $g$ g$. So, in terms of upper bounds, it doesn't really add anything to the function information that $f(x)=cx^{1/2}$ satisfies the inequalityf$ is Hölder continuous of exponent 1/2. |
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We can't decuce too much in terms of upper bounds. Note that for any constant $c\ge0$ and any nonnegative $g$ the function $f(x)=cx^{1/2}$ satisfies the inequality. |
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