Question

$\overline{L^2(\mathbb R)\cap L^1(\mathbb R)}^{L^2(\mathbb R)}=L^2(\mathbb R)$

score 88 · Answer 1 · 2015-05-17 17:11:07

88

Views

$\overline{L^2(\mathbb R)\cap L^1(\mathbb R)}^{L^2(\mathbb R)}=L^2(\mathbb R)$

Published on 17 May 2015 - 17:11

score 279 · Answer 2 · 2015-05-17 20:52:05

279

Views

Inequality leading to Holder's: $t^\theta \leq \theta t + 1 - \theta$ with $0<\theta<1$ and $t\geq 0$

Published on 17 May 2015 - 20:52

score 913 · Answer 3 · 2026-04-02 04:33:26

913

Views

Is $L^1_{loc}(\mathbb{R})$ complete with the norm $|f|=\sup_{x\in \mathbb{R}}\int_x^{x+1}|f(y)|dy$

Published on 02 Apr 2026 - 4:33

score 2.3k · Answer 4 · 2026-04-09 15:18:34

2.3k

Views

Does weak convergence in $W^{1,p}$ imply strong convergence in $L^q$?

Published on 09 Apr 2026 - 15:18

score 68 · Answer 5 · 2026-04-13 16:20:12

68

Views

Why can a function in $L^1(\partial \mathbb{D})$ be represented by a Fourier series?

Published on 13 Apr 2026 - 16:20

score 2.5k · Answer 6 · 2026-04-12 20:28:37

2.5k

Views

Continuity of Translation and Dilation on $L^p$ spaces

Published on 12 Apr 2026 - 20:28

score 222 · Answer 7 · 2026-03-25 21:48:13

222

Views

Partial Fourier series for $L^p$ functions, $p\ge 1$

Published on 25 Mar 2026 - 21:48

score 144 · Answer 8 · 2026-04-09 15:18:32

144

Views

Can we conclude that $v_{n}\rightarrow v$ in $L^{\infty}\left(\Omega\right)$ if $p>N$

Published on 09 Apr 2026 - 15:18

score 2.7k · Answer 9 · 2015-05-21 06:35:10

2.7k

Views

Uniform integrability and weak L1 convergence

Published on 21 May 2015 - 6:35

score 523 · Answer 10 · 2026-04-12 23:10:44

523

Views

Approximate identity for periodic integrable functions

Published on 12 Apr 2026 - 23:10

score 54 · Answer 11 · 2015-05-23 10:02:27

54

Views

If $\sum \|f_n -f \|_{L^1} < \infty$ then $f_n \rightarrow f$ almost uniformly

Published on 23 May 2015 - 10:02

score 1.3k · Answer 12 · 2026-04-10 10:27:04

1.3k

Views

Intuition behind variance in terms of $L^P$ norms?

Published on 10 Apr 2026 - 10:27

score 397 · Answer 13 · 2026-04-14 00:59:10

397

Views

modulation-translation operator continuous in $L^{p}$ norm?

Published on 14 Apr 2026 - 0:59

score 634 · Answer 14 · 2026-04-13 05:51:20

634

Views

L^p spaces are separable and complete but not compact?

Published on 13 Apr 2026 - 5:51

score 558 · Answer 15 · 2015-05-27 12:52:46

558

Views

Predual of $l^1(\Gamma)$

Published on 27 May 2015 - 12:52

List Question

$\overline{L^2(\mathbb R)\cap L^1(\mathbb R)}^{L^2(\mathbb R)}=L^2(\mathbb R)$

Inequality leading to Holder's: $t^\theta \leq \theta t + 1 - \theta$ with $0<\theta<1$ and $t\geq 0$

Is $L^1_{loc}(\mathbb{R})$ complete with the norm $|f|=\sup_{x\in \mathbb{R}}\int_x^{x+1}|f(y)|dy$

Does weak convergence in $W^{1,p}$ imply strong convergence in $L^q$?

Why can a function in $L^1(\partial \mathbb{D})$ be represented by a Fourier series?

Continuity of Translation and Dilation on $L^p$ spaces

Partial Fourier series for $L^p$ functions, $p\ge 1$

Can we conclude that $v_{n}\rightarrow v$ in $L^{\infty}\left(\Omega\right)$ if $p>N$

Uniform integrability and weak L1 convergence

Approximate identity for periodic integrable functions

If $\sum \|f_n -f \|_{L^1} < \infty$ then $f_n \rightarrow f$ almost uniformly

Intuition behind variance in terms of $L^P$ norms?

modulation-translation operator continuous in $L^{p}$ norm?

L^p spaces are separable and complete but not compact?

Predual of $l^1(\Gamma)$

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