Question

Relative inclusion of $L^p$ spaces and norm inequalities.

score 1k · Answer 1 · 2016-08-07 14:58:08

1k

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Relative inclusion of $L^p$ spaces and norm inequalities.

Published on 07 Aug 2016 - 14:58

score 99 · Answer 2 · 2016-08-07 20:32:10

99

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Prove that $E(X+Y)^p \le 2^p (E(X^p)+E(Y^p))$

Published on 07 Aug 2016 - 20:32

score 131 · Answer 3 · 2016-08-08 11:13:01

131

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All the functions $\phi$ such that $\phi (\lim_{p\to 0}||f||_p)=\int_0^1 (\phi of)dm$

Published on 08 Aug 2016 - 11:13

score 177 · Answer 4 · 2026-03-27 22:04:58

177

Views

Given an orthonormal basis $(e_n)_{n\in\mathbb N}$ of $H_0^1(\Lambda)$, construct an orthonormal basis of $H_0^1(\Lambda)^d$

Published on 27 Mar 2026 - 22:04

score 84 · Answer 5 · 2016-08-09 01:42:49

84

Views

Inequality of the $L_p$ spaces

Published on 09 Aug 2016 - 1:42

score 710 · Answer 6 · 2016-08-09 20:06:26

710

Views

let $f$ be a bounded measurable function on $[0,1]$, then $\lim_{p \rightarrow \infty}\|f\|_{p} = \|f\|_{\infty}$.

Published on 09 Aug 2016 - 20:06

score 79 · Answer 7 · 2016-08-10 02:43:49

79

Views

$L^1$ function satisfying extra condition is $L^p$ for $p\in[1,2)$.

Published on 10 Aug 2016 - 2:43

score 861 · Answer 8 · 2016-08-10 15:57:15

861

Views

Density Lp spaces

Published on 10 Aug 2016 - 15:57

score 728 · Answer 9 · 2016-08-10 20:40:56

728

Views

Product of a L^p convergent sequence and pointwise convergence sequece

Published on 10 Aug 2016 - 20:40

score 713 · Answer 10 · 2016-08-11 13:29:19

713

Views

Continuity of the identity map $I:(l^{1},\|.\|_{2})\rightarrow (l^{1},\|.\|_{1}).$

Published on 11 Aug 2016 - 13:29

score 103 · Answer 11 · 2026-03-26 12:33:31

103

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Conclude $u\frac{\partial v}{\partial x_i}\in L^2(\Lambda)$ for all $u,v\in H_0^1(\Lambda)$ from the Sobolev embedding theorem

Published on 26 Mar 2026 - 12:33

score 45 · Answer 12 · 2016-08-12 12:55:45

45

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Finiteness condition for a function in two variables separating them

Published on 12 Aug 2016 - 12:55

score 96 · Answer 13 · 2026-03-27 22:53:00

96

Views

A question on the characterization of the gradient of a distribution

Published on 27 Mar 2026 - 22:53

score 61 · Answer 14 · 2016-08-14 14:27:01

61

Views

Convergence in $L^q$-space

Published on 14 Aug 2016 - 14:27

score 118 · Answer 15 · 2026-04-05 10:09:42

118

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How to integrate by parts with two integrals?

Published on 05 Apr 2026 - 10:09

List Question

Relative inclusion of $L^p$ spaces and norm inequalities.

Prove that $E(X+Y)^p \le 2^p (E(X^p)+E(Y^p))$

All the functions $\phi$ such that $\phi (\lim_{p\to 0}||f||_p)=\int_0^1 (\phi of)dm$

Given an orthonormal basis $(e_n)_{n\in\mathbb N}$ of $H_0^1(\Lambda)$, construct an orthonormal basis of $H_0^1(\Lambda)^d$

Inequality of the $L_p$ spaces

let $f$ be a bounded measurable function on $[0,1]$, then $\lim_{p \rightarrow \infty}\|f\|_{p} = \|f\|_{\infty}$.

$L^1$ function satisfying extra condition is $L^p$ for $p\in[1,2)$.

Density Lp spaces

Product of a L^p convergent sequence and pointwise convergence sequece

Continuity of the identity map $I:(l^{1},\|.\|_{2})\rightarrow (l^{1},\|.\|_{1}).$

Conclude $u\frac{\partial v}{\partial x_i}\in L^2(\Lambda)$ for all $u,v\in H_0^1(\Lambda)$ from the Sobolev embedding theorem

Finiteness condition for a function in two variables separating them

A question on the characterization of the gradient of a distribution

Convergence in $L^q$-space

How to integrate by parts with two integrals?

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