Question

when composition of continuous and Lebesgue integrable function Lebesgue integrable

score 2.2k · Answer 1 · 2026-04-11 02:30:43

2.2k

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when composition of continuous and Lebesgue integrable function Lebesgue integrable

Published on 11 Apr 2026 - 2:30

score 512 · Answer 2 · 2026-04-17 03:17:56

512

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If $f \in L^{p_1}(E) $ is bounded then $f\in L^{p_2}$ for any $p_2>p_1$

Published on 17 Apr 2026 - 3:17

score 184 · Answer 3 · 2026-04-13 11:59:12

184

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There is no bounded linear surjection between $\ell_p$ spaces

Published on 13 Apr 2026 - 11:59

score 69 · Answer 4 · 2026-04-11 08:25:09

69

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Does the norm in $L^p$ has continuity to p?

Published on 11 Apr 2026 - 8:25

score 35 · Answer 5 · 2026-04-16 12:59:14

35

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$f_n\to f$ almost everywhere and $\|f_n\|_{L^2}\to \|f\|_{L^2}$ implies $\|f_n-f\|_{L^2}\to 0$

Published on 16 Apr 2026 - 12:59

score 57 · Answer 6 · 2026-04-16 06:46:20

57

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Normed Linear Space ,$p \neq 2$ is $\left \| f\right \|_{p}= \sqrt{f,f}$ for each $ f \in L^P([0,1])$?

Published on 16 Apr 2026 - 6:46

score 1.3k · Answer 7 · 2026-04-13 13:46:02

1.3k

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Why is this inclusion map continuous?

Published on 13 Apr 2026 - 13:46

score 255 · Answer 8 · 2026-04-11 04:33:58

255

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Is there a way to find the operator norm in this case?

Published on 11 Apr 2026 - 4:33

score 87 · Answer 9 · 2026-04-16 07:46:50

87

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For every $f \in L^1(\mathbb{R})$, do we have $\sup_{n \in \mathbb{N}}|T_nf(x)| < \infty$ for a.e. $x$?

Published on 16 Apr 2026 - 7:46

score 40 · Answer 10 · 2026-04-17 13:27:03

40

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$L^2([-1, 1])$, we have $\lim_{j \to \infty} f_j(x) = 1$ for a.e. $x \in [-1, 1]$?

Published on 17 Apr 2026 - 13:27

score 177 · Answer 11 · 2026-04-16 12:33:13

177

Views

Representing a bounded linear functional on $L^p$

Published on 16 Apr 2026 - 12:33

score 78 · Answer 12 · 2026-04-14 18:46:48

78

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$f \in L^p([0, 1])$, for every $1 \le r < p$, we have $\|f_n - f\|_r \to 0$ as $n \to \infty$.

Published on 14 Apr 2026 - 18:46

score 218 · Answer 13 · 2026-04-16 04:22:03

218

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Partial converse of the fact: $f\in L^p , g\in L^q \Rightarrow fg\in L^1$

Published on 16 Apr 2026 - 4:22

score 388 · Answer 14 · 2026-04-15 16:59:29

388

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Does there exist $f \in L^1(\mathbb{R})$ where $\lim_{r \to 0} {1\over{r}} \int_{x-r}^{x+r} f(y)\,dy = \infty$?

Published on 15 Apr 2026 - 16:59

score 68 · Answer 15 · 2026-04-17 10:10:26

68

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Certain set is dense in $l^p$ if and only if $\{x_n : n \in \mathbb{N}\} \notin l^q$, where $1/p + 1/q = 1$

Published on 17 Apr 2026 - 10:10

List Question

when composition of continuous and Lebesgue integrable function Lebesgue integrable

If $f \in L^{p_1}(E) $ is bounded then $f\in L^{p_2}$ for any $p_2>p_1$

There is no bounded linear surjection between $\ell_p$ spaces

Does the norm in $L^p$ has continuity to p?

$f_n\to f$ almost everywhere and $\|f_n\|_{L^2}\to \|f\|_{L^2}$ implies $\|f_n-f\|_{L^2}\to 0$

Normed Linear Space ,$p \neq 2$ is $\left \| f\right \|_{p}= \sqrt{f,f}$ for each $ f \in L^P([0,1])$?

Why is this inclusion map continuous?

Is there a way to find the operator norm in this case?

For every $f \in L^1(\mathbb{R})$, do we have $\sup_{n \in \mathbb{N}}|T_nf(x)| < \infty$ for a.e. $x$?

$L^2([-1, 1])$, we have $\lim_{j \to \infty} f_j(x) = 1$ for a.e. $x \in [-1, 1]$?

Representing a bounded linear functional on $L^p$

$f \in L^p([0, 1])$, for every $1 \le r < p$, we have $\|f_n - f\|_r \to 0$ as $n \to \infty$.

Partial converse of the fact: $f\in L^p , g\in L^q \Rightarrow fg\in L^1$

Does there exist $f \in L^1(\mathbb{R})$ where $\lim_{r \to 0} {1\over{r}} \int_{x-r}^{x+r} f(y)\,dy = \infty$?

Certain set is dense in $l^p$ if and only if $\{x_n : n \in \mathbb{N}\} \notin l^q$, where $1/p + 1/q = 1$

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