List questions from integral-inequality

222

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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 Apr 2026 - 19:36

85

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

Published on 12 Apr 2026 - 7:36

123

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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 17 Apr 2026 - 14:14

47

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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 16 Apr 2026 - 8:30

32

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Bound the value of function by integration of derivatives

Published on 10 May 2026 - 15:23

1.9k

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

Published on 14 Apr 2026 - 1:10

37

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

Published on 10 May 2026 - 22:04

119

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

Published on 17 Apr 2026 - 2:30

69

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Why does this integral inequality holds?

Published on 12 Apr 2026 - 9:09

128

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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 15 Apr 2026 - 23:59

75

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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 17 Apr 2026 - 1:32

104

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A math inequality cannot prove

Published on 10 Apr 2026 - 8:38

73

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

Published on 16 Apr 2026 - 19:59

126

Views

A singular integral

Published on 10 May 2026 - 16:50

157

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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 17 Apr 2026 - 9:02

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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