Question

Prove that the set of functions $\sin kx$ is closed and bounded

score 155 · Answer 1 · 2017-01-09 19:20:02

155

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Prove that the set of functions $\sin kx$ is closed and bounded

Published on 09 Jan 2017 - 19:20

score 296 · Answer 2 · 2026-04-06 05:16:51

296

Views

Uniform smoothness in $L^p$ via Hanner's inequality

Published on 06 Apr 2026 - 5:16

score 2.7k · Answer 3 · 2017-01-10 08:58:59

2.7k

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$fg\in L^1$ for all $g\in L^q$ $\Longrightarrow f\in L^p$

Published on 10 Jan 2017 - 8:58

score 55 · Answer 4 · 2017-01-10 14:13:57

55

Views

An inequality in $L^p$ spaces

Published on 10 Jan 2017 - 14:13

score 327 · Answer 5 · 2026-04-04 16:16:28

327

Views

Approximating a function in $H^1\cap L^\infty$ by $H^1_0\cap L^\infty$ functions

Published on 04 Apr 2026 - 16:16

score 537 · Answer 6 · 2026-03-28 00:31:00

537

Views

Is the operator $T((x_1,x_2,...,x_n))=(x_1,\frac{x_2}2,\frac{x_3}3,...)$ on $\ell^2$ self-adjoint and unitary

Published on 28 Mar 2026 - 0:31

score 196 · Answer 7 · 2017-01-11 16:11:28

196

Views

$L^p(\mathbb{R})$ is isomterically isomorphic to $L^p((0,1))$

Published on 11 Jan 2017 - 16:11

score 79 · Answer 8 · 2017-01-12 09:50:46

79

Views

$\lim_{p\rightarrow 0}\int_X|f|^p\,d\mu=\mu(\{x\in X\,|\,f(x)\ne 0\})$

Published on 12 Jan 2017 - 9:50

score 160 · Answer 9 · 2017-01-12 13:10:35

160

Views

Is the map $p\mapsto\int_X |f|^p d\mu$ differentiable when $\log|f|\notin L^1$?

Published on 12 Jan 2017 - 13:10

score 58 · Answer 10 · 2026-04-04 16:17:19

58

Views

Deducing $L^4$ convergence in the space-time-cylinder

Published on 04 Apr 2026 - 16:17

score 194 · Answer 11 · 2026-04-07 22:57:55

194

Views

Explicitly demonstrating non-compactness of closed unit ball in $l^{\infty}$

Published on 07 Apr 2026 - 22:57

score 54 · Answer 12 · 2017-01-14 11:04:10

54

Views

If $\mathbb EX_n^2\longrightarrow \mathbb EX^2$ do we have that $X_n\to X$ in $L^2$?

Published on 14 Jan 2017 - 11:04

score 487 · Answer 13 · 2017-01-14 14:28:05

487

Views

Generality about dominated convergence theorem, does $|f_n|\leq g\in L^p$ and $f_n(x)\to f(x)$ a.e. tel us that $f_n\to f$ in $L^p$

Published on 14 Jan 2017 - 14:28

score 42 · Answer 14 · 2026-03-25 04:43:02

42

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$\alpha \in L(L^p, L^{2p})\; \Rightarrow\; \alpha \in L(L^{2p}, L^{4p}), \, p \in [1,\infty)?$

Published on 25 Mar 2026 - 4:43

score 103 · Answer 15 · 2017-01-14 17:00:07

103

Views

Lp spaces examples

Published on 14 Jan 2017 - 17:00

List Question

Prove that the set of functions $\sin kx$ is closed and bounded

Uniform smoothness in $L^p$ via Hanner's inequality

$fg\in L^1$ for all $g\in L^q$ $\Longrightarrow f\in L^p$

An inequality in $L^p$ spaces

Approximating a function in $H^1\cap L^\infty$ by $H^1_0\cap L^\infty$ functions

Is the operator $T((x_1,x_2,...,x_n))=(x_1,\frac{x_2}2,\frac{x_3}3,...)$ on $\ell^2$ self-adjoint and unitary

$L^p(\mathbb{R})$ is isomterically isomorphic to $L^p((0,1))$

$\lim_{p\rightarrow 0}\int_X|f|^p\,d\mu=\mu(\{x\in X\,|\,f(x)\ne 0\})$

Is the map $p\mapsto\int_X |f|^p d\mu$ differentiable when $\log|f|\notin L^1$?

Deducing $L^4$ convergence in the space-time-cylinder

Explicitly demonstrating non-compactness of closed unit ball in $l^{\infty}$

If $\mathbb EX_n^2\longrightarrow \mathbb EX^2$ do we have that $X_n\to X$ in $L^2$?

Generality about dominated convergence theorem, does $|f_n|\leq g\in L^p$ and $f_n(x)\to f(x)$ a.e. tel us that $f_n\to f$ in $L^p$

$\alpha \in L(L^p, L^{2p})\; \Rightarrow\; \alpha \in L(L^{2p}, L^{4p}), \, p \in [1,\infty)?$

Lp spaces examples

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