List questions from lp-spaces

Published on 09 Apr 2026 - 19:13

50

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$S \in \mathcal{L}(L^1(\Omega))$, find $T^* \in \mathcal{L}(L^\infty(\Omega))$ with $T^*g = Sg \forall g \in L^1(\Omega) \cap L^\infty(\Omega)$

Published on 28 Mar 2026 - 14:44

1.1k

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A function $f$ such that $f \in L_1$ but $f \notin L_p$ for $p>1$

Published on 05 Jan 2015 - 1:37

87

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Which is finer(larger) between the sequence spaces $l_{p}$ & $l_{p+1}$

Published on 05 Jan 2015 - 14:58

126

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Characterizing when composition by a power function lies in an $L^p$-space

Published on 12 Apr 2026 - 4:58

41

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If $u \in L^1(0,\infty)$, then $|u(x)| \to 0$ as $x \to \infty$?

Published on 06 Jan 2015 - 13:54

57

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Function in $\mathcal{L}^p(\mu)$ for all $1\leq p \leq 2$

Published on 06 Jan 2015 - 14:14

957

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Completeness of $ L^{p} $ spaces and "rapidly Cauchy" sequences

Published on 12 Apr 2026 - 5:03

272

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L-p space: p-norm proof

Published on 12 Apr 2026 - 19:39

1k

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Problems with the proof that $\ell^p$ is complete

Published on 06 Apr 2026 - 10:40

1.2k

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Almost everywhere convergence of convolution with mollifiers

Published on 12 Apr 2026 - 11:46

92

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If $f \in L^1 \cap L^2$ is $L^2$-differentiable, then $Df \in L^1 \cap L^2$

Published on 08 Jan 2015 - 15:07

313

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Convergence in dual of Sobolev space

Published on 09 Apr 2026 - 13:23

1.9k

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$l^p$ is of first category in $l^q$ if $1 \leq p < q< \infty$

Published on 29 Mar 2026 - 18:34

644

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Sequence is not in any $\ell^p$ space

Published on 09 Jan 2015 - 19:12

List Question

Move Infinite sum inside a limit $t \to \infty$.

$S \in \mathcal{L}(L^1(\Omega))$, find $T^* \in \mathcal{L}(L^\infty(\Omega))$ with $T^*g = Sg \forall g \in L^1(\Omega) \cap L^\infty(\Omega)$

A function $f$ such that $f \in L_1$ but $f \notin L_p$ for $p>1$

Which is finer(larger) between the sequence spaces $l_{p}$ & $l_{p+1}$

Characterizing when composition by a power function lies in an $L^p$-space

If $u \in L^1(0,\infty)$, then $|u(x)| \to 0$ as $x \to \infty$?

Function in $\mathcal{L}^p(\mu)$ for all $1\leq p \leq 2$

Completeness of $ L^{p} $ spaces and "rapidly Cauchy" sequences

L-p space: p-norm proof

Problems with the proof that $\ell^p$ is complete

Almost everywhere convergence of convolution with mollifiers

If $f \in L^1 \cap L^2$ is $L^2$-differentiable, then $Df \in L^1 \cap L^2$

Convergence in dual of Sobolev space

$l^p$ is of first category in $l^q$ if $1 \leq p < q< \infty$

Sequence is not in any $\ell^p$ space

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