List questions from integral-inequality

Published on 27 Mar 2017 - 4:17

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Issue with proof in Folland's 'Real Analysis' (Theorem 6.18)

Published on 30 Mar 2017 - 5:29

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For $0<a<b$ and $n>0$, show that $\left|\int_{a}^b \frac{\cos x}{x^n}\,dx\right|\leq \frac{2}{a^n}.$

Published on 05 Apr 2017 - 17:38

63

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Prove that $\| u\|_{L^2(0,1)}\leq\frac 1 \pi \| u'\|_{L^2(0,1)}$.

Published on 05 Apr 2017 - 18:15

75

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How did this integral inequality come to be?

Published on 06 Apr 2017 - 1:10

2.2k

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Understanding the proof of Holder's inequality(integral version)

Published on 06 Apr 2017 - 7:40

89

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A variant of Cauchy-Schwarz Inequality for integral

Published on 01 Feb 2023 - 9:39

67

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Integral inequality $I_2(z) = \mathcal{O}\left(\frac{1}{(1+z)^2}\right)$

Published on 10 Feb 2023 - 16:09

144

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Upper Bound Product of Integrals

Published on 14 Feb 2023 - 0:26

98

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Energy bound for a closed curve

Published on 16 Feb 2023 - 18:49

169

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Does the $\log$-$\exp$ analogous of Minkowski integral inequality hold true?

Published on 25 Mar 2026 - 12:54

63

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Boundedness of integral operator induced by kernel $K(x,y) := \frac{1}{x+y}$.

Published on 25 Mar 2026 - 6:05

126

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Show that an integral is more than $\frac{\left(\frac{\pi}{2}\right)^{r+1}}{r+2}$

Published on 25 Mar 2023 - 15:09

56

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if $f'(x)<2f(x)$ and $f(\frac{1}{2})=1$ find the interval in which $\int_{\frac{1}{2}}^1 f(x)dx$ lies

Published on 15 Apr 2023 - 10:36

82

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Upper-bound on energy of nonlinear boundary value problem (Hard!)

Published on 28 Apr 2023 - 19:10

List Question

Given $f>0$ can we find $g$ such that $\int g>0$ but $\int fg\le 0$

Issue with proof in Folland's 'Real Analysis' (Theorem 6.18)

For $0<a<b$ and $n>0$, show that $\left|\int_{a}^b \frac{\cos x}{x^n}\,dx\right|\leq \frac{2}{a^n}.$

Prove that $\| u\|_{L^2(0,1)}\leq\frac 1 \pi \| u'\|_{L^2(0,1)}$.

How did this integral inequality come to be?

Understanding the proof of Holder's inequality(integral version)

A variant of Cauchy-Schwarz Inequality for integral

Integral inequality $I_2(z) = \mathcal{O}\left(\frac{1}{(1+z)^2}\right)$

Upper Bound Product of Integrals

Energy bound for a closed curve

Does the $\log$-$\exp$ analogous of Minkowski integral inequality hold true?

Boundedness of integral operator induced by kernel $K(x,y) := \frac{1}{x+y}$.

Show that an integral is more than $\frac{\left(\frac{\pi}{2}\right)^{r+1}}{r+2}$

if $f'(x)<2f(x)$ and $f(\frac{1}{2})=1$ find the interval in which $\int_{\frac{1}{2}}^1 f(x)dx$ lies

Upper-bound on energy of nonlinear boundary value problem (Hard!)

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