Question

Is $\ell_q\subset\ell_p$? What's the "biggest" and "smallest" sequence space?

score 924 · Answer 1 · 2026-04-16 06:16:18

924

Views

Is $\ell_q\subset\ell_p$? What's the "biggest" and "smallest" sequence space?

Published on 16 Apr 2026 - 6:16

score 365 · Answer 2 · 2026-04-13 23:33:51

365

Views

Real Analysis, Folland Problem 6.1.12 $L^p$ spaces

Published on 13 Apr 2026 - 23:33

score 48 · Answer 3 · 2026-04-15 18:49:20

48

Views

If $f_n$ is in $L^1$ and $f_n$ converges to $f$, is $f$ in $L^1$?

Published on 15 Apr 2026 - 18:49

score 1.4k · Answer 4 · 2026-04-12 14:17:15

1.4k

Views

What is duality argument for the operator on $L^p-$ spaces?

Published on 12 Apr 2026 - 14:17

score 24 · Answer 5 · 2026-04-14 18:55:03

24

Views

$C(A)$ is $\|\cdot\|_2$-dense in $\ell_2(A)$

Published on 14 Apr 2026 - 18:55

score 100 · Answer 6 · 2026-04-19 17:16:43

100

Views

$f \in \mathcal l^{\infty}{'} $ ; $f(x)\ge 0$ whenever $x \in \mathcal l^{\infty} $ is a sequence of non-negative terms ; is $f$ bounded?

Published on 19 Apr 2026 - 17:16

score 91 · Answer 7 · 2026-03-27 23:37:55

91

Views

Can we show that each element of the Sobolev space $H^k(D)$, with $D\subseteq\mathbb R^d$ being a bounded domain, has a continuous representative?

Published on 27 Mar 2026 - 23:37

score 93 · Answer 8 · 2026-04-16 20:04:14

93

Views

$f\in L^{1}[0,1]$ Show $\lim_{n\to\infty}\int_{0}^{1}|f(x)|^{\frac{1}{n}}dx = m(\left\{ {x:f(x)\neq 0}\right\} )$

Published on 16 Apr 2026 - 20:04

score 404 · Answer 9 · 2026-04-07 17:47:18

404

Views

$L^p$-norm minimization under linear constraints: Does the optimum depend on $p$?

Published on 07 Apr 2026 - 17:47

score 130 · Answer 10 · 2026-04-16 01:37:40

130

Views

Let $f:\Bbb R \rightarrow \Bbb R$ be a Lebesgue measurable function in $L^2$. Show $F(x)=\int_0^x f(t)dt$ satisfies $|F(x)-F(y)|\leq C|x-y|^\frac 12$

Published on 16 Apr 2026 - 1:37

score 590 · Answer 11 · 2026-04-01 18:51:07

590

Views

Triangle inequality in weak $L^1$ space

Published on 01 Apr 2026 - 18:51

score 74 · Answer 12 · 2026-03-30 10:42:31

74

Views

Given that an integral containing $|x_{n}|$ is bounded by a constant, show that $x_{n}\to x$ in $L^{1}(0,\infty)$

Published on 30 Mar 2026 - 10:42

score 100 · Answer 13 · 2026-04-15 04:53:04

100

Views

Proving that $c_c(\mathbb N)$ is a dense subset of $l^p(\mathbb N)$

Published on 15 Apr 2026 - 4:53

score 462 · Answer 14 · 2026-04-13 07:23:00

462

Views

Real Analysis, Folland Problem 6.1.8 $L^p$ spaces

Published on 13 Apr 2026 - 7:23

score 319 · Answer 15 · 2026-04-14 00:45:08

319

Views

Real Analysis, Folland Problem 6.1.14 $L^p$ spaces

Published on 14 Apr 2026 - 0:45

List Question

Is $\ell_q\subset\ell_p$? What's the "biggest" and "smallest" sequence space?

Real Analysis, Folland Problem 6.1.12 $L^p$ spaces

If $f_n$ is in $L^1$ and $f_n$ converges to $f$, is $f$ in $L^1$?

What is duality argument for the operator on $L^p-$ spaces?

$C(A)$ is $\|\cdot\|_2$-dense in $\ell_2(A)$

$f \in \mathcal l^{\infty}{'} $ ; $f(x)\ge 0$ whenever $x \in \mathcal l^{\infty} $ is a sequence of non-negative terms ; is $f$ bounded?

Can we show that each element of the Sobolev space $H^k(D)$, with $D\subseteq\mathbb R^d$ being a bounded domain, has a continuous representative?

$f\in L^{1}[0,1]$ Show $\lim_{n\to\infty}\int_{0}^{1}|f(x)|^{\frac{1}{n}}dx = m(\left\{ {x:f(x)\neq 0}\right\} )$

$L^p$-norm minimization under linear constraints: Does the optimum depend on $p$?

Let $f:\Bbb R \rightarrow \Bbb R$ be a Lebesgue measurable function in $L^2$. Show $F(x)=\int_0^x f(t)dt$ satisfies $|F(x)-F(y)|\leq C|x-y|^\frac 12$

Triangle inequality in weak $L^1$ space

Given that an integral containing $|x_{n}|$ is bounded by a constant, show that $x_{n}\to x$ in $L^{1}(0,\infty)$

Proving that $c_c(\mathbb N)$ is a dense subset of $l^p(\mathbb N)$

Real Analysis, Folland Problem 6.1.8 $L^p$ spaces

Real Analysis, Folland Problem 6.1.14 $L^p$ spaces

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