Question

Showing that a function lies in $L^p(\mathbb{R}^d)$

score 61 · Answer 1 · 2017-03-15 16:32:12

61

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Showing that a function lies in $L^p(\mathbb{R}^d)$

Published on 15 Mar 2017 - 16:32

score 839 · Answer 2 · 2026-03-26 07:56:42

839

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Compactness in $L^1$ implies equi-integrability

Published on 26 Mar 2026 - 7:56

score 662 · Answer 3 · 2017-03-16 07:18:37

What does a Hamel basis for $L^2([0, 2\pi])$ look like and why is it 'larger' than the set $S = \{\cos(nx), \sin(nx): n \in \mathbb{Z}\}$?

score 1.4k · Answer 4 · 2017-03-16 09:14:14

1.4k

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If $(f_n)\to0$ in $L^2$ and the derivatives converge in $L^2$, must the limit be 0?

Published on 16 Mar 2017 - 9:14

score 38 · Answer 5 · 2026-04-05 18:00:07

38

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When $|\Phi(|x_n|)|\geq 1 \implies |\Phi'(r)|\geq c$ for $r\in (|x_n|-\epsilon, |x_n|+\epsilon)$?

Published on 05 Apr 2026 - 18:00

score 153 · Answer 6 · 2017-03-16 13:48:04

153

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product of weak* convergence and weak convergence in $L^\infty$ and $L^p$

Published on 16 Mar 2017 - 13:48

score 206 · Answer 7 · 2026-04-06 16:55:53

206

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How to prove that a certain subset of $L_p$ space is closed?

Published on 06 Apr 2026 - 16:55

score 181 · Answer 8 · 2017-03-19 16:36:20

181

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Calculate $L^p$ norm

Published on 19 Mar 2017 - 16:36

score 163 · Answer 9 · 2026-04-06 17:51:52

163

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Is $L^1(\mathbb{R}^n)\cap L^2(\mathbb{R}^n)$ dense in $L^2(\mathbb{R}^n)$?

Published on 06 Apr 2026 - 17:51

score 303 · Answer 10 · 2017-03-20 14:17:51

303

Views

Convergence in $L^p(\Bbb R)$

Published on 20 Mar 2017 - 14:17

score 905 · Answer 11 · 2017-03-20 17:46:38

905

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Why is the convolution of two square integrable functions only almost everywhere defined?

Published on 20 Mar 2017 - 17:46

score 2.9k · Answer 12 · 2026-04-05 19:37:20

2.9k

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$H^1$ compactly embedded in weighted $L^2$ space

Published on 05 Apr 2026 - 19:37

score 2.3k · Answer 13 · 2017-03-21 10:01:21

2.3k

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Weak convergence in $L^p(\mathbb{R})$

Published on 21 Mar 2017 - 10:01

score 94 · Answer 14 · 2026-04-06 18:42:28

94

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Show that $\mathcal l^{\infty}$ with norm $\Vert x\Vert = \sup_{k\in \mathbb N}|x_k|$ is Banach space

Published on 06 Apr 2026 - 18:42

score 58 · Answer 15 · 2026-04-06 18:45:14

58

Views

A convergent sequence in $\ell_1$ that is $1/2$-distant to the standard basis

Published on 06 Apr 2026 - 18:45

List Question

Showing that a function lies in $L^p(\mathbb{R}^d)$

Compactness in $L^1$ implies equi-integrability

What does a Hamel basis for $L^2([0, 2\pi])$ look like and why is it 'larger' than the set $S = \{\cos(nx), \sin(nx): n \in \mathbb{Z}\}$?

If $(f_n)\to0$ in $L^2$ and the derivatives converge in $L^2$, must the limit be 0?

When $|\Phi(|x_n|)|\geq 1 \implies |\Phi'(r)|\geq c$ for $r\in (|x_n|-\epsilon, |x_n|+\epsilon)$?

product of weak* convergence and weak convergence in $L^\infty$ and $L^p$

How to prove that a certain subset of $L_p$ space is closed?

Calculate $L^p$ norm

Is $L^1(\mathbb{R}^n)\cap L^2(\mathbb{R}^n)$ dense in $L^2(\mathbb{R}^n)$?

Convergence in $L^p(\Bbb R)$

Why is the convolution of two square integrable functions only almost everywhere defined?

$H^1$ compactly embedded in weighted $L^2$ space

Weak convergence in $L^p(\mathbb{R})$

Show that $\mathcal l^{\infty}$ with norm $\Vert x\Vert = \sup_{k\in \mathbb N}|x_k|$ is Banach space

A convergent sequence in $\ell_1$ that is $1/2$-distant to the standard basis

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