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Results tagged with fa.functional-analysis
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user 41486
Banach spaces, function spaces, real functions, integral transforms, theory of distributions, measure theory.
1
vote
Lipschitz-free spaces of $\mathbb R^n$
I think there are much more elements in $\mathcal F(\mathbb R)$: for example we have $\mathcal{M}(\mathbb R)$ the space of finite measures is in $\mathcal F(\mathbb R)$, but also for every fixed $h \ …
- 151
3
votes
A question on density of Lipschitz functions in weighted Sobolev spaces
The problem is not easy to tackle: a conjecture by De Giorgi was that $e^{w}+ e^{w^{-1}} \in L^1(\mathbb{R}^n)$ is a sufficient condition for the coincidence for general $p$. Recently, in 2013, V.V.Z …
- 151
1
vote
Heat flow $P_tf \to f$ in $W^{1,2}$ for $f \in W^{1,2}$?
There is another approach, maybe more intrinsic, using basically the quadraticity and the lower semicontinuity: we know that $\varepsilon (P_tf)$ is decreasing, in particular $\epsilon (P_t f) \leq \v …
- 151