List questions from lp-spaces

Published on 14 Apr 2026 - 1:36

177

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Convergence in $L^p$ space

Published on 13 Apr 2026 - 12:28

366

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The equality case of Hölder's inequality at the endpoint $p=1$, $q=\infty$

Published on 16 Apr 2026 - 15:59

84

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Function that converges in $L^\infty$ but not in $L^p$

Published on 12 Apr 2026 - 11:05

49

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$L^p(\mathbb{R})$ contains a subspace which is is isometrically isomorphic to $\ell^p$

Published on 15 Apr 2026 - 1:00

187

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convergence in $\ell_{1}$ implies convergence in $\ell_{p}$

Published on 14 Apr 2026 - 14:01

25

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Discontinuities of $u'$ where $u \in W^{1, \infty}([0, T])$

Published on 05 May 2026 - 20:43

68

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Convergence in $L^p$ spaces by subsequences of subsequences

Published on 10 Apr 2026 - 17:24

151

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Does weak convergence in $H^1$ already imply weak convergence in $L^6$ to the same limit?

Published on 05 May 2026 - 20:42

36

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If $f \in L((0,1)^n)$ bounded does follow that $f$ is in $L(\mathbb{R}^n)$?

Published on 16 Apr 2026 - 5:24

34

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Constructing $L^1(\Bbb R^n)$ functions with prescribed properties

Published on 16 Apr 2026 - 3:52

46

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Existence of L2-functions

Published on 13 Apr 2026 - 20:04

162

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pointwise convergence and convergence in $\ell_{1}$ norm

Published on 16 Apr 2026 - 18:58

94

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Showing $\text{range}(A)$ dense: $A: \ell^1 \to \ell^1$, $Ax = \left(\frac{x_n}{n}\right)_{n \in \mathbb{N}}.$

Published on 17 Apr 2026 - 1:34

58

Views

Schauder basis can be uniquely written given a homeomorpism?

Published on 13 Apr 2026 - 20:28

List Question

$L^p(\mu)$ space relations

Convergence in $L^p$ space

The equality case of Hölder's inequality at the endpoint $p=1$, $q=\infty$

Function that converges in $L^\infty$ but not in $L^p$

$L^p(\mathbb{R})$ contains a subspace which is is isometrically isomorphic to $\ell^p$

convergence in $\ell_{1}$ implies convergence in $\ell_{p}$

Discontinuities of $u'$ where $u \in W^{1, \infty}([0, T])$

Convergence in $L^p$ spaces by subsequences of subsequences

Does weak convergence in $H^1$ already imply weak convergence in $L^6$ to the same limit?

If $f \in L((0,1)^n)$ bounded does follow that $f$ is in $L(\mathbb{R}^n)$?

Constructing $L^1(\Bbb R^n)$ functions with prescribed properties

Existence of L2-functions

pointwise convergence and convergence in $\ell_{1}$ norm

Showing $\text{range}(A)$ dense: $A: \ell^1 \to \ell^1$, $Ax = \left(\frac{x_n}{n}\right)_{n \in \mathbb{N}}.$

Schauder basis can be uniquely written given a homeomorpism?

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