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An application of the Closed Graph Theorem

score 49 · Answer 1 · 2026-04-14 06:25:07

49

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An application of the Closed Graph Theorem

Published on 14 Apr 2026 - 6:25

score 145 · Answer 2 · 2026-04-17 12:48:56

145

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If $0 < r < p < \infty$, then $\|f\|_r \leq (\frac{p}{p-r})^{1/r} \mu(X)^{1/r - 1/p} \|f\|_{p, w}$ (weak $L^p$ norm)

Published on 17 Apr 2026 - 12:48

score 32 · Answer 3 · 2026-04-11 03:37:10

32

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What can we say about the bound of a function given its $L^1$ bounds of its partial derivatives

Published on 11 Apr 2026 - 3:37

score 3.8k · Answer 4 · 2026-04-14 19:21:35

3.8k

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If $u \in H^s(\mathbb{R}^n)$ for $s > n/2$, then $u \in L^\infty(\mathbb{R}^n)$?

Published on 14 Apr 2026 - 19:21

score 2.2k · Answer 5 · 2026-03-28 22:24:21

2.2k

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Almost everywhere continuous functions

Published on 28 Mar 2026 - 22:24

score 500 · Answer 6 · 2026-04-11 19:26:34

500

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With regards to a comment on Problem 5.14 from Evans PDE, absolute values.

Published on 11 Apr 2026 - 19:26

score 398 · Answer 7 · 2026-04-13 21:03:18

398

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Trace of multiplication operator on $L^2(\mathbb{T})$

Published on 13 Apr 2026 - 21:03

score 796 · Answer 8 · 2026-04-01 22:24:18

796

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Proving that dual space of $L^\infty(\mathbb{R})$ is not separable

Published on 01 Apr 2026 - 22:24

score 1k · Answer 9 · 2026-04-16 11:16:14

1k

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Proving weak compactness of $L^p$ when $p \neq 1$ or $p \neq \infty$

Published on 16 Apr 2026 - 11:16

score 63 · Answer 10 · 2026-04-16 22:29:43

63

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Approximation of $L^1$ function with compactly supported smooth function with same mass

Published on 16 Apr 2026 - 22:29

score 1.1k · Answer 11 · 2026-04-12 04:12:20

1.1k

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How do I show that $\ell^{\infty}$ is a normed linear space?

Published on 12 Apr 2026 - 4:12

score 1.5k · Answer 12 · 2026-04-14 18:17:59

1.5k

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$L_p$ norm $\leq L_2$ norm for $1\leq p\leq2$ for Random Variables

Published on 14 Apr 2026 - 18:17

score 384 · Answer 13 · 2026-04-12 03:20:17

384

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When we raise $f$ to a positive power, what happens to the norm?

Published on 12 Apr 2026 - 3:20

score 51 · Answer 14 · 2026-04-13 20:59:06

51

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Approximation of $L^1$ function with compactly supported smooth function with same mass and same uniform bounds

Published on 13 Apr 2026 - 20:59

score 55 · Answer 15 · 2026-04-14 04:24:20

55

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Strangely defined ball compact in $L^p(I)$ or not?

Published on 14 Apr 2026 - 4:24

List Question

An application of the Closed Graph Theorem

If $0 < r < p < \infty$, then $\|f\|_r \leq (\frac{p}{p-r})^{1/r} \mu(X)^{1/r - 1/p} \|f\|_{p, w}$ (weak $L^p$ norm)

What can we say about the bound of a function given its $L^1$ bounds of its partial derivatives

If $u \in H^s(\mathbb{R}^n)$ for $s > n/2$, then $u \in L^\infty(\mathbb{R}^n)$?

Almost everywhere continuous functions

With regards to a comment on Problem 5.14 from Evans PDE, absolute values.

Trace of multiplication operator on $L^2(\mathbb{T})$

Proving that dual space of $L^\infty(\mathbb{R})$ is not separable

Proving weak compactness of $L^p$ when $p \neq 1$ or $p \neq \infty$

Approximation of $L^1$ function with compactly supported smooth function with same mass

How do I show that $\ell^{\infty}$ is a normed linear space?

$L_p$ norm $\leq L_2$ norm for $1\leq p\leq2$ for Random Variables

When we raise $f$ to a positive power, what happens to the norm?

Approximation of $L^1$ function with compactly supported smooth function with same mass and same uniform bounds

Strangely defined ball compact in $L^p(I)$ or not?

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