Question

Convergence in $L^q(0,T;L^p(\Omega))$ implies a.e. convergence up to some subsequence?

score 119 · Answer 1 · 2026-03-26 09:41:03

119

Views

Convergence in $L^q(0,T;L^p(\Omega))$ implies a.e. convergence up to some subsequence?

Published on 26 Mar 2026 - 9:41

score 36 · Answer 2 · 2023-11-26 15:29:18

36

Views

$\frac{f}{|x|^4+1}$ lies in $L^1(\mathbb{R}^n) \cap L^2(\mathbb{R}^n)$ for $f \in L^2(\mathbb{R}^n)$ and $n > 6$

Published on 26 Nov 2023 - 15:29

score 63 · Answer 3 · 2023-11-27 05:53:27

63

Views

Is the span of these vectors dense in $L^2(-1,1)$?

Published on 27 Nov 2023 - 5:53

score 20 · Answer 4 · 2026-04-11 23:58:11

20

Views

How to use an interpolation argument to prove $A\hookrightarrow L^p(\mathbb R)$ for $p\in [2, +\infty]?$

Published on 11 Apr 2026 - 23:58

score 96 · Answer 5 · 2023-11-28 10:42:02

96

Views

Correct condition for $L_p$ to be separable.

Published on 28 Nov 2023 - 10:42

score 44 · Answer 6 · 2023-11-28 23:18:14

44

Views

$\lim_{t \to 0} \frac{1}{t^{1/q}}\int_{[0,t]}|f|dm=0$ where $f \in L^{p}$ and $q=p^*$

Published on 28 Nov 2023 - 23:18

score 71 · Answer 7 · 2026-04-10 18:24:59

71

Views

Is this corollary in fact false when $p=1$?

Published on 10 Apr 2026 - 18:24

score 61 · Answer 8 · 2023-12-02 09:44:54

61

Views

$L^1$ and $L^2$ norm inequalities for product of functions

Published on 02 Dec 2023 - 9:44

score 44 · Answer 9 · 2023-12-02 22:04:04

44

Views

For Lebesgue integral theory, whether an integrable sequence of functions converging a.e. converges in L1 under a given "integral finite condition"

Published on 02 Dec 2023 - 22:04

score 171 · Answer 10 · 2023-12-04 04:50:10

171

Views

Counting measure and integrability condition

Published on 04 Dec 2023 - 4:50

score 86 · Answer 11 · 2026-03-26 09:41:53

86

Views

If $\{f_n\}$ is uniformly integrable, then there's a subsequence $(f_{k_n})$ of $(f_n)$ such that $\big(\int _Ef_{k_n}d\mu \big)$ is a Cauchy sequence

Published on 26 Mar 2026 - 9:41

score 68 · Answer 12 · 2026-04-09 00:52:39

68

Views

Is $C[a,b]$ with $p$-norm a normed vectorspace?

Published on 09 Apr 2026 - 0:52

score 39 · Answer 13 · 2023-12-05 13:06:58

39

Views

Struggling to understand why if $|f(x)|\leq 1,|f'(x)|\leq M$ on $[a,b]$ then $\sup|f(x)|\geq 2r$ on interval implies $|f(x)|\geq r$ on that interval

Published on 05 Dec 2023 - 13:06

score 74 · Answer 14 · 2026-04-11 10:55:51

74

Views

The triangle inequality of the $L^p$-norm for a infinite sum

Published on 11 Apr 2026 - 10:55

score 51 · Answer 15 · 2026-03-26 01:27:37

51

Views

Counter example for Riesz representation theorem when $p=\infty$.

Published on 26 Mar 2026 - 1:27

List Question

Convergence in $L^q(0,T;L^p(\Omega))$ implies a.e. convergence up to some subsequence?

$\frac{f}{|x|^4+1}$ lies in $L^1(\mathbb{R}^n) \cap L^2(\mathbb{R}^n)$ for $f \in L^2(\mathbb{R}^n)$ and $n > 6$

Is the span of these vectors dense in $L^2(-1,1)$?

How to use an interpolation argument to prove $A\hookrightarrow L^p(\mathbb R)$ for $p\in [2, +\infty]?$

Correct condition for $L_p$ to be separable.

$\lim_{t \to 0} \frac{1}{t^{1/q}}\int_{[0,t]}|f|dm=0$ where $f \in L^{p}$ and $q=p^*$

Is this corollary in fact false when $p=1$?

$L^1$ and $L^2$ norm inequalities for product of functions

For Lebesgue integral theory, whether an integrable sequence of functions converging a.e. converges in L1 under a given "integral finite condition"

Counting measure and integrability condition

If $\{f_n\}$ is uniformly integrable, then there's a subsequence $(f_{k_n})$ of $(f_n)$ such that $\big(\int _Ef_{k_n}d\mu \big)$ is a Cauchy sequence

Is $C[a,b]$ with $p$-norm a normed vectorspace?

Struggling to understand why if $|f(x)|\leq 1,|f'(x)|\leq M$ on $[a,b]$ then $\sup|f(x)|\geq 2r$ on interval implies $|f(x)|\geq r$ on that interval

The triangle inequality of the $L^p$-norm for a infinite sum

Counter example for Riesz representation theorem when $p=\infty$.

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