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I can't find the counterexample of function with this criteria:

  1. Function $f$ such that $f'$ is absolute continuous in $[a,b]$, $f'' \notin L^2[a,b]$ but $f''$ is bounded in $[a,b]$.

  2. Function $f$ such that $f'$ is absolute continuous in $[a,b]$, $f'' \in L^2[a,b]$ but $f''$ is not bounded in $[a,b]$.

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    If $f''$ is bounded, it must be in $L^2[a,b]$.2012-10-16

1 Answers 1