Question

Convergence in $L^1$ of a sequence of functions

score 106 · Answer 1 · 2026-04-26 14:56:08

106

Views

Convergence in $L^1$ of a sequence of functions

Published on 26 Apr 2026 - 14:56

score 92 · Answer 2 · 2026-04-16 00:46:23

92

Views

Is there a sequence $(f_n)\in\ L^2([0,1])$, s.t. $\lVert f_n\rVert_2=1$, $\forall n$, but it has no convergent subsequences in $L^2([0,1])$ ?

Published on 16 Apr 2026 - 0:46

score 14.5k · Answer 3 · 2026-04-14 06:48:02

14.5k

Views

$L^1$ and $L^{\infty}$ are not reflexive

Published on 14 Apr 2026 - 6:48

score 822 · Answer 4 · 2026-04-12 06:48:59

822

Views

ess-sup property

Published on 12 Apr 2026 - 6:48

score 57 · Answer 5 · 2026-04-15 10:14:20

57

Views

Sufficient and necessary conditions for a given operator $T$ to be $T \in \mathcal{B}$, $T \in \mathcal{K}$ or $T \in \mathcal{F}$

Published on 15 Apr 2026 - 10:14

score 103 · Answer 6 · 2026-04-16 14:06:21

103

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Does $u_n(x) \subset L^p(-1,1)$ converge strongly-weak-weak* to something?

Published on 16 Apr 2026 - 14:06

score 1.1k · Answer 7 · 2026-04-11 20:25:41

1.1k

Views

Integral of $L^2$ function is continuous

Published on 11 Apr 2026 - 20:25

score 315 · Answer 8 · 2026-04-11 05:31:29

315

Views

$L^2$ norm of series with complex exponentials

Published on 11 Apr 2026 - 5:31

score 65 · Answer 9 · 2026-04-16 04:36:14

65

Views

Inequality for the sum of $q$th powers, $1<q<2$

Published on 16 Apr 2026 - 4:36

score 408 · Answer 10 · 2026-04-10 02:15:57

408

Views

Integral of series with complex exponentials

Published on 10 Apr 2026 - 2:15

score 3.7k · Answer 11 · 2026-04-13 12:19:29

3.7k

Views

Fourier transform of convolution for $L^2$ functions

Published on 13 Apr 2026 - 12:19

score 259 · Answer 12 · 2026-04-13 06:56:23

259

Views

Deducing that $f$ is in $L^p$

Published on 13 Apr 2026 - 6:56

score 152 · Answer 13 · 2026-04-14 22:59:53

152

Views

$L^1(\mathbb{R}^n)$ functions not in $\mathcal{H}^1(\mathbb{R}^n)$

Published on 14 Apr 2026 - 22:59

score 1.2k · Answer 14 · 2026-04-14 06:34:13

1.2k

Views

Intuition for a function that belongs to a $L^p$ space

Published on 14 Apr 2026 - 6:34

score 151 · Answer 15 · 2026-04-16 12:42:50

151

Views

Show that if $\lim_{n \to \infty} f_n = 0$ in $\mu$ - measure and $\limsup_{n \to \infty} \int \vert f_n \vert^2 d\mu <1$ \ldots

Published on 16 Apr 2026 - 12:42

List Question

Convergence in $L^1$ of a sequence of functions

Is there a sequence $(f_n)\in\ L^2([0,1])$, s.t. $\lVert f_n\rVert_2=1$, $\forall n$, but it has no convergent subsequences in $L^2([0,1])$ ?

$L^1$ and $L^{\infty}$ are not reflexive

ess-sup property

Sufficient and necessary conditions for a given operator $T$ to be $T \in \mathcal{B}$, $T \in \mathcal{K}$ or $T \in \mathcal{F}$

Does $u_n(x) \subset L^p(-1,1)$ converge strongly-weak-weak* to something?

Integral of $L^2$ function is continuous

$L^2$ norm of series with complex exponentials

Inequality for the sum of $q$th powers, $1<q<2$

Integral of series with complex exponentials

Fourier transform of convolution for $L^2$ functions

Deducing that $f$ is in $L^p$

$L^1(\mathbb{R}^n)$ functions not in $\mathcal{H}^1(\mathbb{R}^n)$

Intuition for a function that belongs to a $L^p$ space

Show that if $\lim_{n \to \infty} f_n = 0$ in $\mu$ - measure and $\limsup_{n \to \infty} \int \vert f_n \vert^2 d\mu <1$ \ldots

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