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Banach spaces, function spaces, real functions, integral transforms, theory of distributions, measure theory.

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Bounding the norm of the Laplacian of the gradient of a function having Lipschitz continuous...

The claim is false. The counter example is the function $f(x) = \varphi(\|x\|_2)$ with an increasing and infinitely differentiable function $\varphi:[0,\infty)\to\mathbb R$ satisfying $$ \varphi(t) = …
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