List questions from integral-inequality

Published on 25 Mar 2026 - 1:36

214

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Does an integral inequality imply a pointwise inequality?

Published on 19 Mar 2026 - 15:32

61

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$|\int_{0}^{x} f(s) ds|^2\leq 2\sqrt{x}\int_{0}^{x} \sqrt{s} |f(s)|^2 ds$

Published on 08 Aug 2018 - 20:06

89

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Prove that $\| \frac{1}{x}\int_{0}^{x} f(s) ds \|_2 \leq 2\|f\|_2$

Published on 08 Aug 2018 - 22:06

302

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Convolution by $\log$ maps $\mathrm{L}^1$ into $\mathrm{BMO}$

Published on 09 Aug 2018 - 4:51

116

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What bound does Chebychev’s inequality give for $P(Y ≥ 3 \text{ or } Y ≤ 1)$?

Published on 09 Aug 2018 - 6:13

207

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Prove that $\int_{0}^{\infty}{e^{-2(m-2)s}(1+s)^m ds}\leq\frac{1}{m-3}$ for $m>3$.

Published on 18 Aug 2018 - 1:33

154

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Is there a good lower bound for the integral $\int_G x^2 \,dx\,dy$ in terms of $\int_G x \,dx\,dy$?

Published on 21 Aug 2018 - 18:28

759

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Do a specific inequality hold under integration?

Published on 22 Aug 2018 - 9:42

43

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Help me understand the expression including operator norm?

Published on 28 Aug 2018 - 4:00

35

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Equality regarding power series and an integral

Published on 24 Mar 2026 - 4:13

547

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On a differential inequality

Published on 29 Aug 2018 - 23:50

110

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How to show that $\int_{t}^{\infty} e^{-\frac{x^2}{2}} dx \leq \frac{1}{t}e^{-\frac{t^2}{2}}$ where $1 \leq t$?

Published on 02 Sep 2018 - 3:33

124

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how to show that $ \frac{\theta e^t(1-\theta)}{(1-\theta+\theta e^t)^2} \leq\frac{1}{4}$?

Published on 22 Mar 2026 - 10:06

42

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Calculating upper bound for increments of a function

Published on 11 Sep 2018 - 11:14

List Question

How to prove positive semi-definiteness or integral inequality

Does an integral inequality imply a pointwise inequality?

$|\int_{0}^{x} f(s) ds|^2\leq 2\sqrt{x}\int_{0}^{x} \sqrt{s} |f(s)|^2 ds$

Prove that $\| \frac{1}{x}\int_{0}^{x} f(s) ds \|_2 \leq 2\|f\|_2$

Convolution by $\log$ maps $\mathrm{L}^1$ into $\mathrm{BMO}$

What bound does Chebychev’s inequality give for $P(Y ≥ 3 \text{ or } Y ≤ 1)$?

Prove that $\int_{0}^{\infty}{e^{-2(m-2)s}(1+s)^m ds}\leq\frac{1}{m-3}$ for $m>3$.

Is there a good lower bound for the integral $\int_G x^2 \,dx\,dy$ in terms of $\int_G x \,dx\,dy$?

Do a specific inequality hold under integration?

Help me understand the expression including operator norm?

Equality regarding power series and an integral

On a differential inequality

How to show that $\int_{t}^{\infty} e^{-\frac{x^2}{2}} dx \leq \frac{1}{t}e^{-\frac{t^2}{2}}$ where $1 \leq t$?

how to show that $ \frac{\theta e^t(1-\theta)}{(1-\theta+\theta e^t)^2} \leq\frac{1}{4}$?

Calculating upper bound for increments of a function

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