List questions from integral-inequality

219

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$\int_0^\pi\left|\frac{\sin {nx}}{x}\right|dx\ge \frac{2}{\pi}\left(1+\frac{1}{2}+\cdots+\frac{1}{n}\right)$

Published on 16 Mar 2020 - 8:31

82

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How to derive an inequality of 1-variable integration involving $f$

Published on 24 Mar 2020 - 8:28

120

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Integral inequality: $3\left(\int_0^1 g(x)^2 dx\right)^3 \geq \int_0^1 g(x)^8 dx.$

Published on 26 Mar 2020 - 6:13

44

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Find $I$ if $\int_0^1 \max\{f(a), f(x)\}dx\ge \max_{x \in I} f(x)$

Published on 27 Mar 2020 - 11:06

31

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Bound the value of function by integration of derivatives

Published on 25 Mar 2026 - 4:39

1.9k

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Embedding Sobolev $H^1$ into $L^\infty$ space

Published on 05 Apr 2020 - 17:28

36

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Immersion $H^s(\Omega) \hookrightarrow H^{s'}(\Omega)$ but with fractional laplacian defined on $\mathbb{R}^N$?

Published on 25 Mar 2026 - 6:29

114

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An integral inequality $f(t)+\int^{\infty}_tg(s)ds\leq Ce^{-\lambda t}$

Published on 10 Apr 2020 - 12:00

66

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Why does this integral inequality holds?

Published on 17 Apr 2020 - 17:23

125

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Show that $\int_0^1|x-\mu|f(x)dx\le \frac{1}{2}, \text { where } \mu=\int_0^1xf(x)dx.$

Published on 20 Apr 2020 - 15:42

72

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Show that $\int_0^1[1+f(x)]dx\int_0^1\frac{1}{1+f(x)}dx\le1.125$

Published on 25 Apr 2020 - 9:58

102

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A math inequality cannot prove

Published on 26 Apr 2020 - 15:17

70

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Prove that $\int_{-a}^{b} x^2f(x)dx\leq ab\int_{-a}^{b}f(x)dx$.

Published on 26 Apr 2020 - 23:54

109

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A singular integral

Published on 26 Mar 2026 - 3:28

154

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Prove $\int_{0}^{1}|f(x)|^2\,dx\le\int_{0}^{1}|f{'}(x)|^2\,dx$ with $f(0)=0$

Published on 27 Apr 2020 - 7:26

List Question

$\int_0^\pi\left|\frac{\sin {nx}}{x}\right|dx\ge \frac{2}{\pi}\left(1+\frac{1}{2}+\cdots+\frac{1}{n}\right)$

How to derive an inequality of 1-variable integration involving $f$

Integral inequality: $3\left(\int_0^1 g(x)^2 dx\right)^3 \geq \int_0^1 g(x)^8 dx.$

Find $I$ if $\int_0^1 \max\{f(a), f(x)\}dx\ge \max_{x \in I} f(x)$

Bound the value of function by integration of derivatives

Embedding Sobolev $H^1$ into $L^\infty$ space

Immersion $H^s(\Omega) \hookrightarrow H^{s'}(\Omega)$ but with fractional laplacian defined on $\mathbb{R}^N$?

An integral inequality $f(t)+\int^{\infty}_tg(s)ds\leq Ce^{-\lambda t}$

Why does this integral inequality holds?

Show that $\int_0^1|x-\mu|f(x)dx\le \frac{1}{2}, \text { where } \mu=\int_0^1xf(x)dx.$

Show that $\int_0^1[1+f(x)]dx\int_0^1\frac{1}{1+f(x)}dx\le1.125$

A math inequality cannot prove

Prove that $\int_{-a}^{b} x^2f(x)dx\leq ab\int_{-a}^{b}f(x)dx$.

A singular integral

Prove $\int_{0}^{1}|f(x)|^2\,dx\le\int_{0}^{1}|f{'}(x)|^2\,dx$ with $f(0)=0$

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