List questions from lp-spaces

Published on 13 Apr 2026 - 13:44

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$L\log L$ and $L^p$ embedding

Published on 14 Apr 2026 - 18:17

50

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Convergence of $L^1$ functions

Published on 14 Apr 2026 - 19:35

8.8k

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Why is $L^{1} \cap L^{\infty}$ dense is in $L^{p}$?

Published on 16 Apr 2026 - 3:04

516

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Embedding of Weak Lebesgue Spaces

Published on 16 Apr 2026 - 13:44

138

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$\mathbb L^1 +$ a.s. convergence of sequence $(X_n)$ does not imply $\sup(x_n)$ is integrable

Published on 18 Apr 2026 - 10:00

91

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$\int_{\mathbb R} |f(x)| dx < \infty \implies \sum_{n\in \mathbb Z} |f(n)| < \infty $?

Published on 16 Apr 2026 - 10:04

86

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Show that H$(I)$ is a closed subspace of $L^2(I)$

Published on 15 Apr 2026 - 3:55

272

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$L^{p}$ inequality with a lower bound on measure

Published on 15 Apr 2026 - 8:44

1.1k

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Limit of $\|x\|_p$ as $p\rightarrow\infty$

Published on 16 Apr 2026 - 3:04

17.3k

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Inclusion of $l^p$ space for sequences

Published on 12 Apr 2026 - 6:48

445

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Implications of Weak convergence in Sobolev Spaces

Published on 25 Apr 2026 - 4:24

237

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Do non-$\ell^2$ sequences have an $\ell^2$ functional that takes them to infinity?

Published on 16 Apr 2026 - 0:05

51

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If $p$, $r$ satisfy $|p|,\, |r| \le 1$ and $1=\lambda p + (1-\lambda)r$ for some $\lambda \in (0,1)$ then $p=r=1$.

Published on 15 Apr 2026 - 1:20

166

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Under what conditions on $f$ does $\|f\|_r = \|f\|_s$ for $0 < r < s < \infty$.

Published on 14 Apr 2026 - 17:40

List Question

Lp space over measure space and over its completion is the same.

$L\log L$ and $L^p$ embedding

Convergence of $L^1$ functions

Why is $L^{1} \cap L^{\infty}$ dense is in $L^{p}$?

Embedding of Weak Lebesgue Spaces

$\mathbb L^1 +$ a.s. convergence of sequence $(X_n)$ does not imply $\sup(x_n)$ is integrable

$\int_{\mathbb R} |f(x)| dx < \infty \implies \sum_{n\in \mathbb Z} |f(n)| < \infty $?

Show that H$(I)$ is a closed subspace of $L^2(I)$

$L^{p}$ inequality with a lower bound on measure

Limit of $\|x\|_p$ as $p\rightarrow\infty$

Inclusion of $l^p$ space for sequences

Implications of Weak convergence in Sobolev Spaces

Do non-$\ell^2$ sequences have an $\ell^2$ functional that takes them to infinity?

If $p$, $r$ satisfy $|p|,\, |r| \le 1$ and $1=\lambda p + (1-\lambda)r$ for some $\lambda \in (0,1)$ then $p=r=1$.

Under what conditions on $f$ does $\|f\|_r = \|f\|_s$ for $0 < r < s < \infty$.

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