Question

Convergence in $L_2$ of sequence of iid variables

score 47 · Answer 1 · 2019-09-09 16:54:40

47

Views

Convergence in $L_2$ of sequence of iid variables

Published on 09 Sep 2019 - 16:54

score 459 · Answer 2 · 2019-09-09 17:12:24

459

Views

Denseness of $L^1\cap L^2$ in $L^p$ on R

Published on 09 Sep 2019 - 17:12

score 209 · Answer 3 · 2019-09-13 17:17:01

209

Views

The density of simple functions in the intersection of mixed norm spaces

Published on 13 Sep 2019 - 17:17

score 166 · Answer 4 · 2026-03-31 07:53:02

166

Views

If $T$ is a bounded linear operator from $L^p(\mathbb{R})$ to $L^q(\mathbb{R})$ and $T$ is non-zero, then $p \leq q$

Published on 31 Mar 2026 - 7:53

score 46 · Answer 5 · 2026-02-23 21:17:30

Any (convergent) sequence of functions in $\mathcal L^p$ that are bounded by a function $w\in\mathcal L^p$ converge in $\mathcal L^p$?

score 264 · Answer 6 · 2019-09-14 15:52:36

264

Views

$\mu(E_{\epsilon})<+\infty$ such that if $F \cap E_{\epsilon} = \emptyset$, then $\left \| f \chi_{F} \right \|_{p} < \epsilon$.

Published on 14 Sep 2019 - 15:52

score 77 · Answer 7 · 2026-03-25 20:33:56

77

Views

Problem of sobolev function in 1d

Published on 25 Mar 2026 - 20:33

score 73 · Answer 8 · 2019-09-15 17:34:29

73

Views

Belonging to a compact convex and weak-* closure

Published on 15 Sep 2019 - 17:34

score 34 · Answer 9 · 2019-09-16 15:47:12

34

Views

if $x_k$ converges in $l^p$, when will $x_ka_k$ converge in $l^q$ and the converse?

Published on 16 Sep 2019 - 15:47

score 188 · Answer 10 · 2026-03-28 14:55:03

188

Views

Approximating $x^2$ by odd powers of $x$ on $\mathbb{R}^+$

Published on 28 Mar 2026 - 14:55

score 36 · Answer 11 · 2019-09-18 12:38:26

36

Views

Differences between $\{ \rho_n \}$ and $ \rho_n $, mollifier

Published on 18 Sep 2019 - 12:38

score 66 · Answer 12 · 2019-09-18 15:26:32

66

Views

Does a function in $L^2(\mathbb{R_+},\mathbb{C}$ necessarily be $0$ at $\pm \infty$?

Published on 18 Sep 2019 - 15:26

score 107 · Answer 13 · 2019-09-18 15:34:29

107

Views

Is the function space in the topological space level?

Published on 18 Sep 2019 - 15:34

score 48 · Answer 14 · 2019-09-19 08:26:07

48

Views

Show that $\left\{\varphi\in{L^p(\mu)}':f(x)\ge\langle\varphi,f\rangle\text{ for all }f\in L^p(\mu)\right\}=\{\delta_x\}$

Published on 19 Sep 2019 - 8:26

score 162 · Answer 15 · 2019-09-21 12:11:16

162

Views

Prove that $f_n \rightharpoonup f$ iff $\sup_n ||f_n||_{L^{p}} < \infty$ in $p \in (1, \infty), f_n,f \in L^p (0,1)$

Published on 21 Sep 2019 - 12:11

List Question

Convergence in $L_2$ of sequence of iid variables

Denseness of $L^1\cap L^2$ in $L^p$ on R

The density of simple functions in the intersection of mixed norm spaces

If $T$ is a bounded linear operator from $L^p(\mathbb{R})$ to $L^q(\mathbb{R})$ and $T$ is non-zero, then $p \leq q$

Any (convergent) sequence of functions in $\mathcal L^p$ that are bounded by a function $w\in\mathcal L^p$ converge in $\mathcal L^p$?

$\mu(E_{\epsilon})<+\infty$ such that if $F \cap E_{\epsilon} = \emptyset$, then $\left \| f \chi_{F} \right \|_{p} < \epsilon$.

Problem of sobolev function in 1d

Belonging to a compact convex and weak-* closure

if $x_k$ converges in $l^p$, when will $x_ka_k$ converge in $l^q$ and the converse?

Approximating $x^2$ by odd powers of $x$ on $\mathbb{R}^+$

Differences between $\{ \rho_n \}$ and $ \rho_n $, mollifier

Does a function in $L^2(\mathbb{R_+},\mathbb{C}$ necessarily be $0$ at $\pm \infty$?

Is the function space in the topological space level?

Show that $\left\{\varphi\in{L^p(\mu)}':f(x)\ge\langle\varphi,f\rangle\text{ for all }f\in L^p(\mu)\right\}=\{\delta_x\}$

Prove that $f_n \rightharpoonup f$ iff $\sup_n ||f_n||_{L^{p}} < \infty$ in $p \in (1, \infty), f_n,f \in L^p (0,1)$

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