Question

banach space bigger than $L^p$

score 82 · Answer 1 · 2026-04-17 18:59:35

82

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banach space bigger than $L^p$

Published on 17 Apr 2026 - 18:59

score 48 · Answer 2 · 2026-04-09 16:45:46

48

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Some insight about this integral limit

Published on 09 Apr 2026 - 16:45

score 348 · Answer 3 · 2026-03-27 15:18:58

348

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Showing that $(G' \circ u)u' \in L^p(I)$ where $G \in C^1(\mathbb{R})$ and $u \in W^{1,p}(I)$

Published on 27 Mar 2026 - 15:18

score 32 · Answer 4 · 2026-04-15 20:07:25

$f_k\rightarrow g$ in $L^p(\mathbb{R}^n)$ and $f_k\rightarrow h$ in $L^r(\mathbb{R}^n)$, then $g=h$ $a.e.$ in $\mathbb{R}^n$

score 80 · Answer 5 · 2026-04-17 15:20:55

80

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Suppose $X_n \to_{p} X$, if $\limsup_n E|X_n|^r \leq E|X|^r$, how can I show that $X_n \to_r X$?

Published on 17 Apr 2026 - 15:20

score 339 · Answer 6 · 2026-04-15 20:14:14

339

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If $\sum_{n=1}^{\infty}x_n^2<\infty$ and $\sum_{m=1}^{\infty}x_n^2<\infty$, is $\sum_{k=1}^{\infty}(x_n)_k^2(x_m)_k^2<\infty$?

Published on 15 Apr 2026 - 20:14

score 42 · Answer 7 · 2026-04-15 23:28:35

42

Views

Inequality for $u \in L^r(\Omega)$: $\int_{\Omega} (a_1+a_2|u|^{r/s})^s dx \leq a_3 \int_{\Omega} (1+|u|^r)dx$

Published on 15 Apr 2026 - 23:28

score 177 · Answer 8 · 2026-04-14 05:36:20

177

Views

Closed subset for $L^2$ strong and weak convergence

Published on 14 Apr 2026 - 5:36

score 526 · Answer 9 · 2026-04-11 17:23:27

526

Views

Triangle inequailty for $L^p$ norm to power $p$

Published on 11 Apr 2026 - 17:23

score 702 · Answer 10 · 2026-04-14 05:00:38

702

Views

Convergence of Riemann sums of a periodic function

Published on 14 Apr 2026 - 5:00

score 333 · Answer 11 · 2026-04-15 19:46:16

333

Views

Proof $\mathcal{C}^1(-1,1)$ is not a closed subspace of Sobolev space $H_0^1 \left[-1,1\right]$

Published on 15 Apr 2026 - 19:46

score 50 · Answer 12 · 2026-04-15 16:43:03

50

Views

$L^2$ convergence by the sequence of domain

Published on 15 Apr 2026 - 16:43

score 71 · Answer 13 · 2026-04-16 10:44:30

71

Views

Prove a vector in $\ell^2(\mathbb{Z})$ is zero

Published on 16 Apr 2026 - 10:44

score 236 · Answer 14 · 2026-04-06 05:15:06

236

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Example of a non square-integrable martingale?

Published on 06 Apr 2026 - 5:15

score 147 · Answer 15 · 2026-04-13 18:28:33

147

Views

What is the parametrization of the set of points in $\mathbb{R}^2$ with $L^p$-(semi)norm $1$ for any $p$?

Published on 13 Apr 2026 - 18:28

List Question

banach space bigger than $L^p$

Some insight about this integral limit

Showing that $(G' \circ u)u' \in L^p(I)$ where $G \in C^1(\mathbb{R})$ and $u \in W^{1,p}(I)$

$f_k\rightarrow g$ in $L^p(\mathbb{R}^n)$ and $f_k\rightarrow h$ in $L^r(\mathbb{R}^n)$, then $g=h$ $a.e.$ in $\mathbb{R}^n$

Suppose $X_n \to_{p} X$, if $\limsup_n E|X_n|^r \leq E|X|^r$, how can I show that $X_n \to_r X$?

If $\sum_{n=1}^{\infty}x_n^2<\infty$ and $\sum_{m=1}^{\infty}x_n^2<\infty$, is $\sum_{k=1}^{\infty}(x_n)_k^2(x_m)_k^2<\infty$?

Inequality for $u \in L^r(\Omega)$: $\int_{\Omega} (a_1+a_2|u|^{r/s})^s dx \leq a_3 \int_{\Omega} (1+|u|^r)dx$

Closed subset for $L^2$ strong and weak convergence

Triangle inequailty for $L^p$ norm to power $p$

Convergence of Riemann sums of a periodic function

Proof $\mathcal{C}^1(-1,1)$ is not a closed subspace of Sobolev space $H_0^1 \left[-1,1\right]$

$L^2$ convergence by the sequence of domain

Prove a vector in $\ell^2(\mathbb{Z})$ is zero

Example of a non square-integrable martingale?

What is the parametrization of the set of points in $\mathbb{R}^2$ with $L^p$-(semi)norm $1$ for any $p$?

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