Question

Infinite Matrices from $l^p$ to $l^{\frac{p}{p-1}}$ that are compact operators

score 78 · Answer 1 · 2026-04-14 10:47:41

78

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Infinite Matrices from $l^p$ to $l^{\frac{p}{p-1}}$ that are compact operators

Published on 14 Apr 2026 - 10:47

score 56 · Answer 2 · 2026-04-16 01:41:42

56

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let $X$ be of a finite measure & $f\in L^1$, $f(x) \neq 0$ a.e. Show if $E \subset X$: $ \lim_{n \to \infty} \int_E|f|^{1/n} d\mu = \mu(E)$

Published on 16 Apr 2026 - 1:41

score 190 · Answer 3 · 2026-04-11 06:26:10

190

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Sections, Projections, and Polars of $\ell_p$ Balls

Published on 11 Apr 2026 - 6:26

score 150 · Answer 4 · 2026-04-10 08:46:53

150

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Are squares of square integrable functions square integrable?

Published on 10 Apr 2026 - 8:46

score 44 · Answer 5 · 2026-04-16 09:12:48

44

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Is the Integral Operator $L_p(\mathbb{R}^n)\ni\varphi\mapsto \int_{\mathbb{R}^n} \varphi (x) g(x) dx, g\in L_{p'}(\mathbb{R}^n)$ (Frechet-) Smooth?

Published on 16 Apr 2026 - 9:12

score 90 · Answer 6 · 2026-04-15 21:59:25

90

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If $p<q$, then $L^q\subset L^p+L^\infty$

Published on 15 Apr 2026 - 21:59

score 68 · Answer 7 · 2026-04-15 10:26:41

68

Views

L2 convergence of weighted iid normal distribution

Published on 15 Apr 2026 - 10:26

score 91 · Answer 8 · 2026-04-14 03:30:04

91

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Does $f(x)=\frac{1}{x^{2}}$ define a distribution on $\mathbb{R}$?

Published on 14 Apr 2026 - 3:30

score 236 · Answer 9 · 2026-04-29 11:21:45

236

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Inequality of Lp-norm with supremum

Published on 29 Apr 2026 - 11:21

score 65 · Answer 10 · 2026-04-11 12:33:11

65

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How to prove this conclusion in Real Analysis?

Published on 11 Apr 2026 - 12:33

score 65 · Answer 11 · 2026-04-15 06:41:55

65

Views

L^1 approximation of Dirac measure are not in L^p

Published on 15 Apr 2026 - 6:41

score 330 · Answer 12 · 2026-04-15 03:28:41

330

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$L^p(\Omega)$ is separable for $1 \leq p <\infty$

Published on 15 Apr 2026 - 3:28

score 55 · Answer 13 · 2026-04-18 06:11:16

55

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Connection between the cumulative distribution function and $p$-integrability

Published on 18 Apr 2026 - 6:11

score 91 · Answer 14 · 2026-04-16 02:41:07

91

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Theorem 4.14 in Brézis book

Published on 16 Apr 2026 - 2:41

score 47 · Answer 15 · 2026-04-17 00:06:56

47

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If $O_a=\{f \in L^\infty(\Omega):\|f-u_a\|_\infty<\frac{1}{2}\}$ then $O_a \cap O_b=\emptyset$ if $a \neq b$

Published on 17 Apr 2026 - 0:06

List Question

Infinite Matrices from $l^p$ to $l^{\frac{p}{p-1}}$ that are compact operators

let $X$ be of a finite measure & $f\in L^1$, $f(x) \neq 0$ a.e. Show if $E \subset X$: $ \lim_{n \to \infty} \int_E|f|^{1/n} d\mu = \mu(E)$

Sections, Projections, and Polars of $\ell_p$ Balls

Are squares of square integrable functions square integrable?

Is the Integral Operator $L_p(\mathbb{R}^n)\ni\varphi\mapsto \int_{\mathbb{R}^n} \varphi (x) g(x) dx, g\in L_{p'}(\mathbb{R}^n)$ (Frechet-) Smooth?

If $p<q$, then $L^q\subset L^p+L^\infty$

L2 convergence of weighted iid normal distribution

Does $f(x)=\frac{1}{x^{2}}$ define a distribution on $\mathbb{R}$?

Inequality of Lp-norm with supremum

How to prove this conclusion in Real Analysis?

L^1 approximation of Dirac measure are not in L^p

$L^p(\Omega)$ is separable for $1 \leq p <\infty$

Connection between the cumulative distribution function and $p$-integrability

Theorem 4.14 in Brézis book

If $O_a=\{f \in L^\infty(\Omega):\|f-u_a\|_\infty<\frac{1}{2}\}$ then $O_a \cap O_b=\emptyset$ if $a \neq b$

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