List questions from lp-spaces

Published on 14 Apr 2026 - 2:27

113

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Convolution of $L^1 \cap L^q$ and $L^2 \cap L^{\infty}$

Published on 16 Apr 2026 - 9:19

437

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Reflexivity and Separability of $L^{\infty}$ and $L^{1}$

Published on 11 Apr 2026 - 16:57

30

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Royden 8.2 - Criterion for convergence in $L^2(E)$

Published on 15 Apr 2026 - 14:34

75

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Norm of linear functional on product space

Published on 10 Apr 2026 - 5:14

181

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Matrix representation of operators on $\ell^2$.

Published on 11 May 2026 - 5:19

38

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Limit of a sequence in $l^p$

Published on 15 Apr 2026 - 22:59

158

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How can I show that the Sobolev space $W_p^1 (a,b)$ is closed?

Published on 14 Apr 2026 - 15:03

195

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Bounded linear functional attaining its norm on a $\sigma$-finite measure space

Published on 12 Apr 2026 - 0:55

416

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$f_n(x) = n^{1/p}\chi(nx)$ in $L^p(\mathbb{R})$ weakly converges to 0 for $1 \leq p <\infty$

Published on 17 Apr 2026 - 7:50

155

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Showing $L^{\infty}(\mathbb R)^\neq L^1(\mathbb R)$ using the weak star compactness of unit ball in $L^{\infty}(\mathbb R)^$.

Published on 15 Apr 2026 - 20:57

101

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Prove that $\|f\|_{L^\infty(\Omega)}=\sup\{\lambda:\mu \{ x: |f(x)|>\lambda \}>0\} $

Published on 15 Apr 2026 - 14:08

223

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Does the constant in Poincaré inequality (for $W^{1,p}_0$) depend on $p$?

Published on 14 May 2026 - 19:34

305

Views

Convergence in $L^2$ doesn't imply uniform convergence

Published on 14 May 2026 - 6:18

64

Views

Is a zero sequence in $L^1$ eventually in $L^p$ for each $p>1$?

Published on 15 Apr 2026 - 23:35

List Question

Bounded linear functionals on $L^p(\mathbb{R})$, $0<p<1$.

Convolution of $L^1 \cap L^q$ and $L^2 \cap L^{\infty}$

Reflexivity and Separability of $L^{\infty}$ and $L^{1}$

Royden 8.2 - Criterion for convergence in $L^2(E)$

Norm of linear functional on product space

Matrix representation of operators on $\ell^2$.

Limit of a sequence in $l^p$

How can I show that the Sobolev space $W_p^1 (a,b)$ is closed?

Bounded linear functional attaining its norm on a $\sigma$-finite measure space

$f_n(x) = n^{1/p}\chi(nx)$ in $L^p(\mathbb{R})$ weakly converges to 0 for $1 \leq p <\infty$

Showing $L^{\infty}(\mathbb R)^\neq L^1(\mathbb R)$ using the weak star compactness of unit ball in $L^{\infty}(\mathbb R)^$.

Prove that $\|f\|_{L^\infty(\Omega)}=\sup\{\lambda:\mu \{ x: |f(x)|>\lambda \}>0\} $

Does the constant in Poincaré inequality (for $W^{1,p}_0$) depend on $p$?

Convergence in $L^2$ doesn't imply uniform convergence

Is a zero sequence in $L^1$ eventually in $L^p$ for each $p>1$?

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