List questions from lp-spaces

Published on 30 Sep 2023 - 18:42

36

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Mixed norm estimate for $L^p$-functions

Published on 03 Oct 2023 - 13:13

178

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A proof of Poincare inequality

Published on 07 Apr 2026 - 9:42

55

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If $f, f^2, \nabla f^2 \in L^2$, what can you say about $\nabla f$?

Published on 04 Oct 2023 - 20:54

51

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Prove that $L^p\left ( \mathbb R^n, e^{\frac{-1}2 |x|^2} \right)\cap \theta(\mathbb R^n)$ is infinite dimensional

Published on 30 Mar 2026 - 15:14

35

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Prove that u(x) is in $L^{\infty}\left(B(0,1)\right)$

Published on 07 Oct 2023 - 13:56

79

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Brezis' exercise 8.2.1: a bounded sequence in $W^{1, p}(I)$

Published on 26 Mar 2026 - 14:42

82

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Asymptotic formula for the $L^2$ norm of a periodic function

Published on 11 Apr 2026 - 15:39

76

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Brezis' exercise 8.3: Helly’s selection theorem

Published on 07 Apr 2026 - 9:36

32

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Sequence of smooth compactly supported function on a bounded open set which converge to the signum of the difference of two functions

Published on 09 Oct 2023 - 14:45

99

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$\|f \otimes g\|_{L^p} \leq \|f\|_{L^p} \|g\|_{L^p}$ for $1 \leq p \leq \infty$

Published on 26 Mar 2026 - 8:00

52

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Brezis' exercise 8.6.1: $W^{2, p} (I) \subset C^1 (\bar I)$ with compact injection for $p \in (1, \infty]$

Published on 07 Apr 2026 - 11:17

32

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Let $I=(0, 1)$. The injection $W^{2, 1}(I) \subset W^{1, 1}(I)$ is compact

Published on 07 Apr 2026 - 11:17

54

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Brezis' exercise 8.6.3: is there a shorter approach?

Published on 06 Apr 2026 - 16:16

48

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Brezis' exercise 8.6.4: the injection $W^{m, p}(I) \subset C^{m-1}(\bar I)$ is compact for $m \ge 2$ and $p \in (1, \infty]$

Published on 07 Apr 2026 - 11:18

List Question

Separability of $L^p(\mathbb R^n ,\mu)$

Mixed norm estimate for $L^p$-functions

A proof of Poincare inequality

If $f, f^2, \nabla f^2 \in L^2$, what can you say about $\nabla f$?

Prove that $L^p\left ( \mathbb R^n, e^{\frac{-1}2 |x|^2} \right)\cap \theta(\mathbb R^n)$ is infinite dimensional

Prove that u(x) is in $L^{\infty}\left(B(0,1)\right)$

Brezis' exercise 8.2.1: a bounded sequence in $W^{1, p}(I)$

Asymptotic formula for the $L^2$ norm of a periodic function

Brezis' exercise 8.3: Helly’s selection theorem

Sequence of smooth compactly supported function on a bounded open set which converge to the signum of the difference of two functions

$\|f \otimes g\|_{L^p} \leq \|f\|_{L^p} \|g\|_{L^p}$ for $1 \leq p \leq \infty$

Brezis' exercise 8.6.1: $W^{2, p} (I) \subset C^1 (\bar I)$ with compact injection for $p \in (1, \infty]$

Let $I=(0, 1)$. The injection $W^{2, 1}(I) \subset W^{1, 1}(I)$ is compact

Brezis' exercise 8.6.3: is there a shorter approach?

Brezis' exercise 8.6.4: the injection $W^{m, p}(I) \subset C^{m-1}(\bar I)$ is compact for $m \ge 2$ and $p \in (1, \infty]$

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