Question

Generalization of Cauchy-Schwarz/Hölder inequality

score 320 · Answer 1 · 2026-05-14 09:59:47

320

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Generalization of Cauchy-Schwarz/Hölder inequality

Published on 14 May 2026 - 9:59

score 70 · Answer 2 · 2026-04-17 07:31:11

70

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For finite-duration continuous $f(t)$ with $\|f'(t)\|_\infty < \infty$: It is true $\|f'(t)\|_\infty \leq \frac{2\pi \|f'(t)\|_2^2}{\|f'(t)\|_1}$?

Published on 17 Apr 2026 - 7:31

score 67 · Answer 3 · 2026-04-14 11:15:49

67

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Function $f\in L^1(\mathbb{R})$ which is absolutely continous but $f'\notin L^1(\mathbb{R})$

Published on 14 Apr 2026 - 11:15

score 166 · Answer 4 · 2026-05-06 11:32:25

166

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If the inner product induces the l2 norm, what kind of non-inner product induces a general Lp norm where $p \neq 2$?

Published on 06 May 2026 - 11:32

score 124 · Answer 5 · 2026-05-14 09:56:59

124

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Find $p$ such that the integral is finite

Published on 14 May 2026 - 9:56

score 47 · Answer 6 · 2026-04-18 21:16:23

47

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How to see or prove $L_p(\mathbb R^{n+1})= t^{-\frac{n+1}{p}}L_p(\mathbb R_+\times S^n ,\frac{dt}{t}d\phi)$

Published on 18 Apr 2026 - 21:16

score 140 · Answer 7 · 2026-04-15 23:04:37

140

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Show that if $f_n\to f_1$ uniformly and $f_n\to f_2$ in $L^p$, then $f_1=f_2$ almost everywhere.

Published on 15 Apr 2026 - 23:04

score 49 · Answer 8 · 2026-04-12 19:35:29

49

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Question on an inequality concerning integrals.

Published on 12 Apr 2026 - 19:35

score 158 · Answer 9 · 2026-04-11 19:07:34

158

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Does the finite sequence belong to $\ell^p$?

Published on 11 Apr 2026 - 19:07

score 65 · Answer 10 · 2026-04-16 06:06:14

65

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If $\varphi, g$ are positive and non-zero in $L^p(\mathbb R^n)$ and $L^q(\mathbb R^n)$ respectively, then so is their product in $L^1(\mathbb R^n)$

Published on 16 Apr 2026 - 6:06

score 129 · Answer 11 · 2026-04-17 00:31:47

129

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Prove that $\lim_{n\to\infty}\|f_n-f\|_p=\lim_{n\to\infty}\|g_n-g\|_p=0$

Published on 17 Apr 2026 - 0:31

score 158 · Answer 12 · 2026-04-14 23:43:24

158

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Proving that $L^1(X,M,\mu)$ is not reflexive

Published on 14 Apr 2026 - 23:43

score 146 · Answer 13 · 2026-04-17 04:48:54

146

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Subset of $\ell^2$ which is closed and bounded, but not compact

Published on 17 Apr 2026 - 4:48

score 141 · Answer 14 · 2026-04-16 10:28:59

141

Views

How to prove $\|f*g\|_1 \leq \|f\|_1 \cdot \|g\|_1$

Published on 16 Apr 2026 - 10:28

score 191 · Answer 15 · 2026-04-14 18:01:39

191

Views

Average of a $L^p$ function in the ball $B_r(x) \subset \mathbb{R}^n$ using convolution results

Published on 14 Apr 2026 - 18:01

List Question

Generalization of Cauchy-Schwarz/Hölder inequality

For finite-duration continuous $f(t)$ with $\|f'(t)\|_\infty < \infty$: It is true $\|f'(t)\|_\infty \leq \frac{2\pi \|f'(t)\|_2^2}{\|f'(t)\|_1}$?

Function $f\in L^1(\mathbb{R})$ which is absolutely continous but $f'\notin L^1(\mathbb{R})$

If the inner product induces the l2 norm, what kind of non-inner product induces a general Lp norm where $p \neq 2$?

Find $p$ such that the integral is finite

How to see or prove $L_p(\mathbb R^{n+1})= t^{-\frac{n+1}{p}}L_p(\mathbb R_+\times S^n ,\frac{dt}{t}d\phi)$

Show that if $f_n\to f_1$ uniformly and $f_n\to f_2$ in $L^p$, then $f_1=f_2$ almost everywhere.

Question on an inequality concerning integrals.

Does the finite sequence belong to $\ell^p$?

If $\varphi, g$ are positive and non-zero in $L^p(\mathbb R^n)$ and $L^q(\mathbb R^n)$ respectively, then so is their product in $L^1(\mathbb R^n)$

Prove that $\lim_{n\to\infty}\|f_n-f\|_p=\lim_{n\to\infty}\|g_n-g\|_p=0$

Proving that $L^1(X,M,\mu)$ is not reflexive

Subset of $\ell^2$ which is closed and bounded, but not compact

How to prove $\|f*g\|_1 \leq \|f\|_1 \cdot \|g\|_1$

Average of a $L^p$ function in the ball $B_r(x) \subset \mathbb{R}^n$ using convolution results

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