Question

Lebesgue spaces $\mathscr{L}^{p}$ for $p<1$

score 97 · Answer 1 · 2023-11-26 12:57:40

97

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Lebesgue spaces $\mathscr{L}^{p}$ for $p<1$

Published on 26 Nov 2023 - 12:57

score 145 · Answer 2 · 2026-03-25 16:20:53

145

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How to prove $\frac{1}{\sqrt{14a^2+b^2+c^2}}+\frac{1}{\sqrt{14b^2+a^2+c^2}}+\frac{1}{\sqrt{14c^2+b^2+a^2}}\ge \frac{9}{4(a+b+c)}$?

Published on 25 Mar 2026 - 16:20

score 102 · Answer 3 · 2026-03-25 16:20:53

102

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How to prove $\frac{1}{\sqrt{3a^2+13b}}+\frac{1}{\sqrt{3b^2+13c}}+\frac{1}{\sqrt{3c^2+13a}} \ge \frac{3}{4}$?

Published on 25 Mar 2026 - 16:20

score 14 · Answer 4 · 2023-11-29 20:03:01

14

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Packing problem in the 3D cube - generalisation of the Loomis-Whitney / Finner / Brascamp–Lieb / Holder inequality

Published on 29 Nov 2023 - 20:03

score 53 · Answer 5 · 2023-11-30 14:06:28

53

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Dual function non-overlapping Group Lasso's penalty function

Published on 30 Nov 2023 - 14:06

score 73 · Answer 6 · 2026-03-26 08:02:28

73

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Inequality $\frac{1}{\sqrt{4a^2+4b^2+17ab}}+\frac{1}{\sqrt{4b^2+4c^2+17bc}}+\frac{1}{\sqrt{4c^2+4a^2+17ca}}\ge \frac{3}{5}. $

Published on 26 Mar 2026 - 8:02

score 165 · Answer 7 · 2026-03-26 08:02:37

165

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Inequality $\frac{1}{\sqrt{ab+2}}+\frac{1}{\sqrt{bc+2}}+\frac{1}{\sqrt{ca+2}}\ge \frac{2\sqrt{3}}{\sqrt{a+b+c+abc}}.$

Published on 26 Mar 2026 - 8:02

score 168 · Answer 8 · 2023-12-06 13:25:23

168

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Conjecture on the representation of $\log$-convex functions

Published on 06 Dec 2023 - 13:25

score 38 · Answer 9 · 2023-12-10 21:38:56

38

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Hoelder's inequality for measurable functions alone?

Published on 10 Dec 2023 - 21:38

score 71 · Answer 10 · 2023-12-12 08:25:09

If $a^2+b^2+c^2=9$ prove $\frac{1}{\sqrt[3]{a^3+b^3}}+\frac{1}{\sqrt[3]{c^3+b^3}}+\frac{1}{\sqrt[3]{a^3+c^3}}\ge \sqrt[3]{\frac{a+b+c}{2}}. $

score 88 · Answer 11 · 2023-12-26 19:49:11

88

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How to use Lebesgue Number for Complex Analysis Holder Inequality

Published on 26 Dec 2023 - 19:49

score 91 · Answer 12 · 2024-01-02 07:26:22

91

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$\frac{a}{\sqrt{2a^2+3bc}}+\frac{b}{\sqrt{2b^2+3ca}}+\frac{c}{\sqrt{2c^2+3ab}} \le \sqrt{ab+bc+ca}$

Published on 02 Jan 2024 - 7:26

score 183 · Answer 13 · 2024-01-13 18:41:47

183

Views

If $u \notin L^p[0,1]$, can we find some $w \in L^{\frac{p}{p-1}}[0,1]$ such that $\int_0^1 u \cdot w = \infty$?

Published on 13 Jan 2024 - 18:41

score 198 · Answer 14 · 2024-01-17 13:10:30

198

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Showing $\frac{1}{5}<(f(k,l,m,n))^3\leq\frac{64}{11}$, where $f(k,l,m,n)=\sum_{cyc}\frac{k^2}{\sqrt[3]{5k^6+6l^3m^3}}$ for positive $k$, $l$, $m$, $n$

Published on 17 Jan 2024 - 13:10

score 67 · Answer 15 · 2024-01-23 22:42:56

67

Views

For which $p\in [1,+\infty]$ is the following operator continuous?

Published on 23 Jan 2024 - 22:42

List Question

Lebesgue spaces $\mathscr{L}^{p}$ for $p<1$

How to prove $\frac{1}{\sqrt{14a^2+b^2+c^2}}+\frac{1}{\sqrt{14b^2+a^2+c^2}}+\frac{1}{\sqrt{14c^2+b^2+a^2}}\ge \frac{9}{4(a+b+c)}$?

How to prove $\frac{1}{\sqrt{3a^2+13b}}+\frac{1}{\sqrt{3b^2+13c}}+\frac{1}{\sqrt{3c^2+13a}} \ge \frac{3}{4}$?

Packing problem in the 3D cube - generalisation of the Loomis-Whitney / Finner / Brascamp–Lieb / Holder inequality

Dual function non-overlapping Group Lasso's penalty function

Inequality $\frac{1}{\sqrt{4a^2+4b^2+17ab}}+\frac{1}{\sqrt{4b^2+4c^2+17bc}}+\frac{1}{\sqrt{4c^2+4a^2+17ca}}\ge \frac{3}{5}. $

Inequality $\frac{1}{\sqrt{ab+2}}+\frac{1}{\sqrt{bc+2}}+\frac{1}{\sqrt{ca+2}}\ge \frac{2\sqrt{3}}{\sqrt{a+b+c+abc}}.$

Conjecture on the representation of $\log$-convex functions

Hoelder's inequality for measurable functions alone?

If $a^2+b^2+c^2=9$ prove $\frac{1}{\sqrt[3]{a^3+b^3}}+\frac{1}{\sqrt[3]{c^3+b^3}}+\frac{1}{\sqrt[3]{a^3+c^3}}\ge \sqrt[3]{\frac{a+b+c}{2}}. $

How to use Lebesgue Number for Complex Analysis Holder Inequality

$\frac{a}{\sqrt{2a^2+3bc}}+\frac{b}{\sqrt{2b^2+3ca}}+\frac{c}{\sqrt{2c^2+3ab}} \le \sqrt{ab+bc+ca}$

If $u \notin L^p[0,1]$, can we find some $w \in L^{\frac{p}{p-1}}[0,1]$ such that $\int_0^1 u \cdot w = \infty$?

Showing $\frac{1}{5}<(f(k,l,m,n))^3\leq\frac{64}{11}$, where $f(k,l,m,n)=\sum_{cyc}\frac{k^2}{\sqrt[3]{5k^6+6l^3m^3}}$ for positive $k$, $l$, $m$, $n$

For which $p\in [1,+\infty]$ is the following operator continuous?

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