List questions from lp-spaces

Published on 13 Apr 2026 - 2:34

28

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If ${\mathbb E} [f(x)] < \infty$, does $\|f(x)p(x)\|_{q}$ hold for $q \in [1, \infty]$? Note: $p(x)$ is the pdf of $X$.

Published on 16 Apr 2026 - 14:04

1.3k

Views

"Norm is continuous" means?

Published on 12 Apr 2026 - 1:25

234

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interchanging limits

Published on 24 Apr 2026 - 17:50

102

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Convergence in Sobolev spaces 2

Published on 25 Apr 2026 - 12:19

158

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Estimate for convolution

Published on 14 Apr 2026 - 0:14

30

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Check basic argument about convergence in $L^2$ and pointwise convergence

Published on 16 Apr 2026 - 2:46

112

Views

If $f\in L^{\infty}(E)$,then $\|f\|_{ \infty}=\lim_{p\to \infty}\|f\|_{ p}$.

Published on 15 Apr 2026 - 20:08

748

Views

Proving Subspace of $L^2$ and orthogonal complement

Published on 16 Apr 2026 - 4:52

84

Views

$(X,m)$ be a measure space ; how to show that for $1 \le p \le \infty$ , $L^p(X,m)$ is a Hilbert space iff $p=2$?

Published on 14 Apr 2026 - 15:55

39

Views

Needs clarification in a proof--

Published on 12 Apr 2026 - 19:59

60

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Is $L^p$ isomorphic to $l^p$?

Published on 15 Apr 2026 - 13:44

413

Views

What is the difference of - $L^p$ spaces - defined using extended real line and real line functions?

Published on 15 Apr 2026 - 2:02

86

Views

Complete measure spaces and convergence in $L^p(\mu)$

Published on 13 Apr 2026 - 3:29

153

Views

The equality of Sobolev norm and Lebesgue norm, $\|v\|_{-2} = \|v\|_{L^2}$

Published on 25 Apr 2026 - 14:04

List Question

Closed subspaces of $L^{\infty}[0,1]$

If ${\mathbb E} [f(x)] < \infty$, does $\|f(x)p(x)\|_{q}$ hold for $q \in [1, \infty]$? Note: $p(x)$ is the pdf of $X$.

"Norm is continuous" means?

interchanging limits

Convergence in Sobolev spaces 2

Estimate for convolution

Check basic argument about convergence in $L^2$ and pointwise convergence

If $f\in L^{\infty}(E)$,then $\|f\|_{ \infty}=\lim_{p\to \infty}\|f\|_{ p}$.

Proving Subspace of $L^2$ and orthogonal complement

$(X,m)$ be a measure space ; how to show that for $1 \le p \le \infty$ , $L^p(X,m)$ is a Hilbert space iff $p=2$?

Needs clarification in a proof--

Is $L^p$ isomorphic to $l^p$?

What is the difference of - $L^p$ spaces - defined using extended real line and real line functions?

Complete measure spaces and convergence in $L^p(\mu)$

The equality of Sobolev norm and Lebesgue norm, $\|v\|_{-2} = \|v\|_{L^2}$

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