List questions from holder-inequality

42

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Prove that $||x||_{p} \leq ||x||_{q} \cdot d^{(1/p) - (1/q)}$, if $1 < p < q $ for any $x \in \mathbb R^{d}$

Published on 25 Mar 2026 - 17:42

41

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prove integrable functions by means of Holder inequality

Published on 25 Mar 2026 - 17:38

240

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Let $a, b, c, d \in R^+$ such that $a + b + c + d = 1$. Prove that $\frac{a^3}{b+c}+\frac{b^3}{c+d}+\frac{c^3}{d+a}+\frac{d^3}{a+b} \geq \frac{1}{8}$

Published on 25 Mar 2026 - 17:41

188

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Lp spaces and Hölder Inequality

Published on 25 Mar 2026 - 17:38

42

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If $ x \in \mathbb R^n$ with $\|x\|_\infty < 1$, how to make sense of this quantity $W(x):= \sum_{p=1}^\infty\|x\|_p^p$?

Published on 25 Mar 2026 - 19:06

274

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Jensen inequality in measure theory : why doesn't the convex function need to be nonnegative?

Published on 25 Mar 2026 - 19:04

242

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Prove that the cyclic sum over $a, b, c > 0$ $ \sum (\frac{a}{a+b})^3 >= \frac{3}{8}$

Published on 25 Mar 2026 - 22:06

157

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Inequality on ratio of norms

Published on 25 Mar 2026 - 17:40

60

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Proving that an inequality holds

Published on 25 Mar 2026 - 17:38

439

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IMO $2001$ problem $2$

Published on 26 Apr 2026 - 10:57

102

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Hölder's inequality for $\frac{1}{\sqrt{a}} + \frac{1}{\sqrt{b}} + \frac{1}{\sqrt{c}}$

Published on 25 Mar 2026 - 19:06

174

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Question on Hölder's inequality when it's equal

Published on 25 Mar 2026 - 17:38

118

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On Resolving a Fuss on Squares and Fractions over a few Inequalities

Published on 09 Apr 2026 - 9:35

95

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Inequality involving medians

Published on 25 Mar 2026 - 17:38

927

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Understanding reverse Hölder and Minkowski inequalities

Published on 25 Mar 2026 - 17:38

List Question

Prove that $||x||_{p} \leq ||x||_{q} \cdot d^{(1/p) - (1/q)}$, if $1 < p < q $ for any $x \in \mathbb R^{d}$

prove integrable functions by means of Holder inequality

Let $a, b, c, d \in R^+$ such that $a + b + c + d = 1$. Prove that $\frac{a^3}{b+c}+\frac{b^3}{c+d}+\frac{c^3}{d+a}+\frac{d^3}{a+b} \geq \frac{1}{8}$

Lp spaces and Hölder Inequality

If $ x \in \mathbb R^n$ with $\|x\|_\infty < 1$, how to make sense of this quantity $W(x):= \sum_{p=1}^\infty\|x\|_p^p$?

Jensen inequality in measure theory : why doesn't the convex function need to be nonnegative?

Prove that the cyclic sum over $a, b, c > 0$ $ \sum (\frac{a}{a+b})^3 >= \frac{3}{8}$

Inequality on ratio of norms

Proving that an inequality holds

IMO $2001$ problem $2$

Hölder's inequality for $\frac{1}{\sqrt{a}} + \frac{1}{\sqrt{b}} + \frac{1}{\sqrt{c}}$

Question on Hölder's inequality when it's equal

On Resolving a Fuss on Squares and Fractions over a few Inequalities

Inequality involving medians

Understanding reverse Hölder and Minkowski inequalities

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