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

1 vote

Equivalence of Sobolev spaces for different metrics

You said you know why the $L^2$ norms are equivalent, so let's look at the gradient term $$\int |\nabla^{g_1}u|^2,$$ where the norm associated to $|\cdot|$ doesn't matter. But since $u$ is a function, …
Ryan Unger's user avatar