List questions from lp-spaces

Published on 30 Mar 2026 - 14:38

167

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If the sum of two independent random variables is in $L^2$, is it true that both of them are in $L^1$?

Published on 12 May 2014 - 20:56

2.2k

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Bound on uniform norm of convolution of $L^p$ functions

Published on 28 Mar 2026 - 2:42

230

Views

function $L_p$ iff $1\leq p<2$

Published on 14 May 2014 - 13:17

1.4k

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Is Lp space complete with this norm?

Published on 30 Mar 2026 - 16:22

568

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show that $x$ is in $\ell^1$ if $\sum x_ny_n$ is convergent for all $y=(y_n)\in{c_0}$

Published on 14 May 2014 - 16:39

106

Views

An $L^2$ bound for a function of the form $w(x)=|x|^{-1} - (g^2|x|^{-1}g^2)(x)$

Published on 30 Mar 2026 - 5:29

81

Views

How to give a criterion for strong convergence of in $L_p[0,1]$ for this example

Published on 17 May 2014 - 17:38

125

Views

How to show that the sequence $(x^{(n)})$ weakly convergent in $l_p$, $1\le p\lt \infty$

Published on 30 Mar 2026 - 3:20

73

Views

Prove that $||f||_2 \le \sqrt{2 \pi} ||f || _{\infty}$

Published on 30 Mar 2026 - 21:11

632

Views

Is a non-compact Riemannian manifold a "measure space"?

Published on 20 May 2014 - 20:31

166

Views

Proof verification-density of smooth compactly supported functions

Published on 20 May 2014 - 21:36

92

Views

Am I wrong ? (2)

Published on 30 Mar 2026 - 16:20

74

Views

a question about $L^p$ functions on domains in Euclidean spaces

Published on 23 May 2014 - 7:08

88

Views

Sequence of continuous functions with unitary norm

Published on 30 Mar 2026 - 17:54

List Question

Nontrivial functionals on $l^\infty$ vanishing on $c_0$

If the sum of two independent random variables is in $L^2$, is it true that both of them are in $L^1$?

Bound on uniform norm of convolution of $L^p$ functions

function $L_p$ iff $1\leq p<2$

Is Lp space complete with this norm?

show that $x$ is in $\ell^1$ if $\sum x_ny_n$ is convergent for all $y=(y_n)\in{c_0}$

An $L^2$ bound for a function of the form $w(x)=|x|^{-1} - (g^2|x|^{-1}g^2)(x)$

How to give a criterion for strong convergence of in $L_p[0,1]$ for this example

How to show that the sequence $(x^{(n)})$ weakly convergent in $l_p$, $1\le p\lt \infty$

Prove that $||f||_2 \le \sqrt{2 \pi} ||f || _{\infty}$

Is a non-compact Riemannian manifold a "measure space"?

Proof verification-density of smooth compactly supported functions

Am I wrong ? (2)

a question about $L^p$ functions on domains in Euclidean spaces

Sequence of continuous functions with unitary norm

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