List questions from lp-spaces

Published on 12 Apr 2026 - 11:49

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The $L^p(\mathbb R)$ norm is increasing as a function of $p$ (Update: It's false!)

Published on 11 Apr 2026 - 11:20

145

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The function $\phi(p)=\|f\|_{L^p}^p$ is convex

Published on 24 Apr 2015 - 9:21

417

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Rudin Real & Complex Analysis Thm 3.14

Published on 13 Apr 2026 - 19:32

1.3k

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Convergence of $ L^{p} $-integrals implies convergence in $ L^{p} $-norm?

Published on 13 Apr 2026 - 6:50

865

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$L^{1} \cap L^{\infty}$ is dense is in $L^{p}$

Published on 26 Apr 2015 - 16:37

162

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Need help understanding this proof of a certain inequality of $L^p$ norms.

Published on 12 Apr 2026 - 0:19

1.8k

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Can $ {L^{1}}(G) $ be a $ C^{*} $-algebra?

Published on 28 Mar 2026 - 19:39

508

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The norm $\|f_n-f\|_{L^1} \to 0$ but $f_n \not\to f$

Published on 28 Apr 2015 - 3:54

404

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Why is it important that $L^P$ spaces be complete?

Published on 11 Apr 2026 - 20:12

91

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How does $\inf_{c \in \mathbb{R}} \lVert u - c \rVert_{L^2} \le \lVert \nabla u \rVert_{L^2}$ imply this inequality?

Published on 31 Mar 2026 - 7:52

603

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Holder Inequality when $0 < p < 1$

Published on 29 Apr 2015 - 5:26

1.1k

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Proving that the dual of $\ell^p$ is $\ell^\infty$ for $0<p<1$.

Published on 30 Apr 2015 - 2:39

45

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Showing $f$ is integrable on a plane, given a bound on its $L^{3/2}$ norm on certain regions

Published on 11 Apr 2026 - 19:35

38.2k

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Show that $l^2$ is a Hilbert space

Published on 12 Apr 2026 - 5:44

List Question

Intuition behind the Riesz-Thorin interpolation theorem

The $L^p(\mathbb R)$ norm is increasing as a function of $p$ (Update: It's false!)

The function $\phi(p)=\|f\|_{L^p}^p$ is convex

Rudin Real & Complex Analysis Thm 3.14

Convergence of $ L^{p} $-integrals implies convergence in $ L^{p} $-norm?

$L^{1} \cap L^{\infty}$ is dense is in $L^{p}$

Need help understanding this proof of a certain inequality of $L^p$ norms.

Can $ {L^{1}}(G) $ be a $ C^{*} $-algebra?

The norm $\|f_n-f\|_{L^1} \to 0$ but $f_n \not\to f$

Why is it important that $L^P$ spaces be complete?

How does $\inf_{c \in \mathbb{R}} \lVert u - c \rVert_{L^2} \le \lVert \nabla u \rVert_{L^2}$ imply this inequality?

Holder Inequality when $0 < p < 1$

Proving that the dual of $\ell^p$ is $\ell^\infty$ for $0<p<1$.

Showing $f$ is integrable on a plane, given a bound on its $L^{3/2}$ norm on certain regions

Show that $l^2$ is a Hilbert space

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