Question

Three equivalent inequalities with $ \rho :\ \mathbb{R}\to [0,+\infty ),\ \int_{-\infty }^{+\infty } \rho(t) \mathrm{d}t=1$

score 63 · Answer 1 · 2021-09-19 04:25:46

63

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Three equivalent inequalities with $ \rho :\ \mathbb{R}\to [0,+\infty ),\ \int_{-\infty }^{+\infty } \rho(t) \mathrm{d}t=1$

Published on 19 Sep 2021 - 4:25

score 33 · Answer 2 · 2021-10-06 03:22:44

33

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Showing that an integral estimate is best possible

Published on 06 Oct 2021 - 3:22

score 71 · Answer 3 · 2021-10-07 20:42:07

71

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Estimating $\int_0^{2\pi}\left(\sum_{n=1}^{N} \cos (n^2x) \right)^4\ dx$ for large $N$

Published on 07 Oct 2021 - 20:42

score 106 · Answer 4 · 2021-10-12 07:32:46

106

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How to prove integral inequality using Cauchy-Schwarz

Published on 12 Oct 2021 - 7:32

score 20 · Answer 5 · 2026-03-25 23:36:54

20

Views

Convexity of a function defined on $W^{1,p}(]0,r[)$

Published on 25 Mar 2026 - 23:36

score 88 · Answer 6 · 2026-03-27 14:03:27

88

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Does Hölder's Inequality implies that $\int_{-\infty}^\infty |f(t) \,g(t)|\,\mathrm dt \leq \int_{-\infty}^\infty |f(t)|\,\mathrm dt \, \sup |g|$?

Published on 27 Mar 2026 - 14:03

score 129 · Answer 7 · 2021-10-25 19:07:48

129

Views

Hanner inequality: reduction to non-negative functions

Published on 25 Oct 2021 - 19:07

score 48 · Answer 8 · 2021-10-28 21:21:09

48

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Define $g(n) = \int_{-\infty}^{\infty} dx |h(x)|^{n} e^{-f(x)}.$ Must $g(n)$ be between $g(n-1)$ and $g(n+1)$?

Published on 28 Oct 2021 - 21:21

score 1.3k · Answer 9 · 2021-10-31 17:42:14

1.3k

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A detailed proof of Minkowski's inequality for integrals

Published on 31 Oct 2021 - 17:42

score 193 · Answer 10 · 2026-03-27 02:06:50

193

Views

Counterexample to Jensen's inequality?

Published on 27 Mar 2026 - 2:06

score 106 · Answer 11 · 2021-11-16 13:46:58

106

Views

If $f(t)$ fulfill $\int_{-\infty}^\infty |f(t)|dt < \infty$, Is then true $\int_{-\infty}^\infty |f(t)|^2 dt < \infty$? If not, What else is needed?

Published on 16 Nov 2021 - 13:46

score 838 · Answer 12 · 2021-11-17 03:48:51

838

Views

How to understand correctly the differential inequalities?

Published on 17 Nov 2021 - 3:48

score 151 · Answer 13 · 2021-11-18 13:43:55

151

Views

Application of Cauchy-Schwarz to improper integrals

Published on 18 Nov 2021 - 13:43

score 45 · Answer 14 · 2021-11-21 09:27:09

45

Views

How does one explain this inequality which swaps integral and product?

Published on 21 Nov 2021 - 9:27

score 207 · Answer 15 · 2021-11-26 15:39:35

207

Views

$L^2$ norm and $L^{\infty}$ inequality for periodic smooth functions

Published on 26 Nov 2021 - 15:39

List Question

Three equivalent inequalities with $ \rho :\ \mathbb{R}\to [0,+\infty ),\ \int_{-\infty }^{+\infty } \rho(t) \mathrm{d}t=1$

Showing that an integral estimate is best possible

Estimating $\int_0^{2\pi}\left(\sum_{n=1}^{N} \cos (n^2x) \right)^4\ dx$ for large $N$

How to prove integral inequality using Cauchy-Schwarz

Convexity of a function defined on $W^{1,p}(]0,r[)$

Does Hölder's Inequality implies that $\int_{-\infty}^\infty |f(t) \,g(t)|\,\mathrm dt \leq \int_{-\infty}^\infty |f(t)|\,\mathrm dt \, \sup |g|$?

Hanner inequality: reduction to non-negative functions

Define $g(n) = \int_{-\infty}^{\infty} dx |h(x)|^{n} e^{-f(x)}.$ Must $g(n)$ be between $g(n-1)$ and $g(n+1)$?

A detailed proof of Minkowski's inequality for integrals

Counterexample to Jensen's inequality?

If $f(t)$ fulfill $\int_{-\infty}^\infty |f(t)|dt < \infty$, Is then true $\int_{-\infty}^\infty |f(t)|^2 dt < \infty$? If not, What else is needed?

How to understand correctly the differential inequalities?

Application of Cauchy-Schwarz to improper integrals

How does one explain this inequality which swaps integral and product?

$L^2$ norm and $L^{\infty}$ inequality for periodic smooth functions

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