List questions from integral-inequality

Published on 29 Jan 2021 - 19:30

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Vector norm of integral inequality

Published on 02 Feb 2021 - 15:25

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Calculation of $\int_a^b f(x)\,dx$

Published on 08 Feb 2021 - 8:59

68

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Lebesgue integration : Inequality

Published on 08 Feb 2021 - 10:33

55

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Do we have a version of Grönwall lemma for $t<b$?

Published on 08 Feb 2021 - 12:19

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Prove inequality involving integral

Published on 09 Feb 2021 - 16:07

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Given two positive numbers $x,y.$ Prove that $\left|x\ln x-y\ln y\right|\leq\sqrt[3]{\left|x^{2}-y^{2}\right|}+\sqrt[3]{\left|x^{2}-y^{2}\right|^{2}}$

Published on 19 Feb 2021 - 9:58

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Sine Fourier coefficients of derivative

Published on 24 Feb 2021 - 11:12

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Prove or disprove that $f\left(x\right)\leq 1,$ which is a continuous function so that $\int_0^x tf\left(2x-t\right){\rm d}t=\frac{\tan^{-1}x^2}{2}$

Published on 26 Feb 2021 - 2:24

117

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Upper bound for a Fresnel Integral

Published on 05 Mar 2021 - 23:52

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Prove that $\int_0^a |f(x)|^2|f'(x)|dx \le \frac{a^2}{3}\int_0^a |f'(x)|^3dx$

Published on 12 Mar 2021 - 20:41

120

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An $L^1$ estimates related to Fejer Kernels

Published on 15 Mar 2021 - 12:07

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$f:[-1,1]\to\Bbb{R}$ be continuous and $\int_{-1}^{1}f(t)dt=1$ then find $\displaystyle \lim_{n\to \infty} \int f(t) \cos^2nt \mathrm{d}t$.[NBHM2008]

Published on 17 Mar 2021 - 7:28

89

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Proof or counterexample to $ \int_a^t |f(x)|dx \leq \sup_t|\int f(x)dx| $

Published on 26 Mar 2021 - 18:31

181

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Does an asymptotic vanishing of Jensen gap imply that the variance tend to zero?

Published on 01 Apr 2021 - 9:25

List Question

Is $\int_{0}^{1}\frac{\|f\|_{L^p(0,x)}}{x}dx $ controlled by $\|f\|_{L^p(0,1)}$

Vector norm of integral inequality

Calculation of $\int_a^b f(x)\,dx$

Lebesgue integration : Inequality

Do we have a version of Grönwall lemma for $t<b$?

Prove inequality involving integral

Given two positive numbers $x,y.$ Prove that $\left|x\ln x-y\ln y\right|\leq\sqrt[3]{\left|x^{2}-y^{2}\right|}+\sqrt[3]{\left|x^{2}-y^{2}\right|^{2}}$

Sine Fourier coefficients of derivative

Prove or disprove that $f\left(x\right)\leq 1,$ which is a continuous function so that $\int_0^x tf\left(2x-t\right){\rm d}t=\frac{\tan^{-1}x^2}{2}$

Upper bound for a Fresnel Integral

Prove that $\int_0^a |f(x)|^2|f'(x)|dx \le \frac{a^2}{3}\int_0^a |f'(x)|^3dx$

An $L^1$ estimates related to Fejer Kernels

$f:[-1,1]\to\Bbb{R}$ be continuous and $\int_{-1}^{1}f(t)dt=1$ then find $\displaystyle \lim_{n\to \infty} \int f(t) \cos^2nt \mathrm{d}t$.[NBHM2008]

Proof or counterexample to $ \int_a^t |f(x)|dx \leq \sup_t|\int f(x)dx| $

Does an asymptotic vanishing of Jensen gap imply that the variance tend to zero?

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