List questions from holder-inequality

Published on 04 Apr 2026 - 2:22

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If $\lim \int_0^1 |f_n(x)|=0$ and $|f_n|^2\leq g$ where g is integrable on [0,1], then $\lim \int_0^1 |f_n|^2=0$

Published on 25 Mar 2026 - 12:50

1.4k

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Prove that $(x + \sqrt[3]{abc})^3 \le (x + a)(x + b)(x + c) \le ( x + \frac{a + b + c}{3})^3$

Published on 25 Mar 2026 - 16:03

93

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Proving an interesting inequality with square roots

Published on 13 Apr 2026 - 1:26

850

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Prove that the minimum values of $x^2+y^2+z^2$ is $27$ with given condition $\dfrac{1}{x}+\dfrac{1}{y}+\dfrac{1}{z}=1$.

Published on 10 May 2026 - 16:35

108

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Hölder inequality with Lebesgue measure

Published on 25 Mar 2026 - 12:48

58

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if $\mu(X)=1$ , $f\in L^1$, then $f\in L^\infty$?

Published on 25 Mar 2026 - 19:10

103

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Inequality $\sum_{cyc} \sqrt{\frac{a}{b+c+d}}>2$

Published on 25 Mar 2026 - 12:52

110

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$a, b, c$ are three reals such that $ab + bc + ca = 3abc$. Prove that $\sum_{cyc}\sqrt{2(a + b)} \ge \sum_{cyc}\sqrt{\frac{a^2 + b^2}{a + b}} + 3$.

Published on 25 Mar 2026 - 12:50

85

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Prove inequality by inequality of means

Published on 25 Mar 2026 - 12:53

37

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show that $\|f\|_p = \max_{g\in L^q(E)\\\|g\|_q\le 1} \int_E f.g~d\mu$

Published on 25 Mar 2026 - 19:06

59

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if $\{f_n\}\to f$ in $L^{p_2}(E)$ then $\{f_n\}\to f$ in $L^{p_1}(E)$.

Published on 25 Mar 2026 - 12:51

186

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Show that for $p>1,$ $\mathbb{E}[Y^p] \leq \big(\frac{p}{p-1}\big)^p\mathbb{E}[X^p]$

Published on 25 Mar 2026 - 12:54

49

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How to prove this inequality with exponents?

Published on 25 Mar 2026 - 12:55

329

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Holder inequality with $q = \infty$

Published on 25 Mar 2026 - 16:06

List Question

Does Holder's inequality require finite measure space?

If $\lim \int_0^1 |f_n(x)|=0$ and $|f_n|^2\leq g$ where g is integrable on [0,1], then $\lim \int_0^1 |f_n|^2=0$

Prove that $(x + \sqrt[3]{abc})^3 \le (x + a)(x + b)(x + c) \le ( x + \frac{a + b + c}{3})^3$

Proving an interesting inequality with square roots

Prove that the minimum values of $x^2+y^2+z^2$ is $27$ with given condition $\dfrac{1}{x}+\dfrac{1}{y}+\dfrac{1}{z}=1$.

Hölder inequality with Lebesgue measure

if $\mu(X)=1$ , $f\in L^1$, then $f\in L^\infty$?

Inequality $\sum_{cyc} \sqrt{\frac{a}{b+c+d}}>2$

$a, b, c$ are three reals such that $ab + bc + ca = 3abc$. Prove that $\sum_{cyc}\sqrt{2(a + b)} \ge \sum_{cyc}\sqrt{\frac{a^2 + b^2}{a + b}} + 3$.

Prove inequality by inequality of means

show that $\|f\|_p = \max_{g\in L^q(E)\\\|g\|_q\le 1} \int_E f.g~d\mu$

if $\{f_n\}\to f$ in $L^{p_2}(E)$ then $\{f_n\}\to f$ in $L^{p_1}(E)$.

Show that for $p>1,$ $\mathbb{E}[Y^p] \leq \big(\frac{p}{p-1}\big)^p\mathbb{E}[X^p]$

How to prove this inequality with exponents?

Holder inequality with $q = \infty$

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