List questions from lp-spaces

77

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Showing $u_{\lambda}(x):= \left(\frac{\lambda}{{\lambda}^{2}+|x|^2}\right)^{\frac{n-2}{2}}$ is not sequentially compact in $L^{2^{*}}$

Published on 22 Mar 2026 - 18:49

478

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Exercise 7.19 from Papa Rudin: Gathering solutions

Published on 19 Mar 2026 - 15:41

69

Views

Measure inequality in $L^2$

Published on 16 Mar 2026 - 21:08

43

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Which of the following functions are in $L^p(\Omega)$

Published on 17 Mar 2026 - 11:03

661

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$L^1$ is not reflexive

Published on 16 Mar 2026 - 21:43

128

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Is it a equivalent semi norm in Campanato space?

Published on 23 Mar 2026 - 10:54

87

Views

Sufficient conditions on $F$ such that $F(X)\in\mathcal{L}^{p}$ for all $X\in\mathcal{L}^{p}$

Published on 27 Jan 2018 - 12:01

321

Views

Are the canonical representatives of the Hilbert space $L^2$ basis-dependent?

Published on 27 Jan 2018 - 20:44

62

Views

Proving a property of a $L^1(\mu)$ function.

Published on 17 Mar 2026 - 9:10

523

Views

Is the square of an $H^1$ function also $H^1$?

Published on 22 Mar 2026 - 23:08

59

Views

Show that $p\mapsto ||X||_p$ is nondecreasing for $p\in (0,\infty]$

Published on 17 Mar 2026 - 22:15

747

Views

$C^\infty_0$ approximation of $L^\infty$

Published on 22 Mar 2026 - 18:41

105

Views

Example of integrable function which is nowhere $p$-integrable

Published on 19 Mar 2026 - 19:46

105

Views

Is $\ell^1(\mathbb{N})^*$ separable? If so, why?

Published on 23 Mar 2026 - 1:02

906

Views

Dense subspaces of $L^\infty(\Omega\times\Omega)$

Published on 23 Mar 2026 - 7:12

List Question

Showing $u_{\lambda}(x):= \left(\frac{\lambda}{{\lambda}^{2}+|x|^2}\right)^{\frac{n-2}{2}}$ is not sequentially compact in $L^{2^{*}}$

Exercise 7.19 from Papa Rudin: Gathering solutions

Measure inequality in $L^2$

Which of the following functions are in $L^p(\Omega)$

$L^1$ is not reflexive

Is it a equivalent semi norm in Campanato space?

Sufficient conditions on $F$ such that $F(X)\in\mathcal{L}^{p}$ for all $X\in\mathcal{L}^{p}$

Are the canonical representatives of the Hilbert space $L^2$ basis-dependent?

Proving a property of a $L^1(\mu)$ function.

Is the square of an $H^1$ function also $H^1$?

Show that $p\mapsto ||X||_p$ is nondecreasing for $p\in (0,\infty]$

$C^\infty_0$ approximation of $L^\infty$

Example of integrable function which is nowhere $p$-integrable

Is $\ell^1(\mathbb{N})^*$ separable? If so, why?

Dense subspaces of $L^\infty(\Omega\times\Omega)$

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