Question

$f, g$ measurable, $\lVert g\rVert_1=1$ and $0 \le a \le f \le b$ so $\int_{\mathbb{R^n}} \frac{g}{f}dx \ge \frac{1}{\int_{\mathbb{R^n}} fg dx}$

score 24 · Answer 1 · 2021-02-14 15:03:30

24

Views

$f, g$ measurable, $\lVert g\rVert_1=1$ and $0 \le a \le f \le b$ so $\int_{\mathbb{R^n}} \frac{g}{f}dx \ge \frac{1}{\int_{\mathbb{R^n}} fg dx}$

Published on 14 Feb 2021 - 15:03

score 203 · Answer 2 · 2021-02-15 11:23:48

203

Views

Algebraic inequality $\sum \frac{x^3}{(x+y)(x+z)(x+t)}\geq \frac{1}{2}$

Published on 15 Feb 2021 - 11:23

score 17 · Answer 3 · 2021-02-17 09:33:35

17

Views

Let $f, g :(0,1) \to \mathbb{R}\,\,$ s.t. $\lVert g \rVert_2 =3$ and $\lVert f \rVert_1 = e\,\,$, show that $|\int_{0}^{1} g \sqrt{\log(f)}dx| \le 3$

Published on 17 Feb 2021 - 9:33

score 75 · Answer 4 · 2021-02-17 21:58:51

75

Views

Kind of equality on the sphere in Holder inequality

Published on 17 Feb 2021 - 21:58

score 191 · Answer 5 · 2021-02-18 04:42:58

191

Views

An interpolation inequality using Holder inequality

Published on 18 Feb 2021 - 4:42

score 99 · Answer 6 · 2021-02-25 07:19:30

99

Views

$\sum\sqrt{\frac{2a}{b+c}}\le\sqrt[3]{9\sum\frac{a}{b}}$

Published on 25 Feb 2021 - 7:19

score 38 · Answer 7 · 2021-03-13 18:59:40

38

Views

$f^{p_1}$ belongs to $L^p(E)$ and $g = \chi_{E}$ belongs to $L^q(E)$?

Published on 13 Mar 2021 - 18:59

score 119 · Answer 8 · 2021-03-13 19:24:51

119

Views

Vectorial $L^p$ spaces

Published on 13 Mar 2021 - 19:24

score 307 · Answer 9 · 2026-03-25 11:16:23

307

Views

Application of Hölder's inequality: $(a+b)^t \le 2^t(a^t+b^t)$ for $t\ge 1.$

Published on 25 Mar 2026 - 11:16

score 71 · Answer 10 · 2021-03-31 21:23:16

71

Views

Prove that $\cup_{1<p\leq\infty} L^p([0,1])\subset L^1([0,1]) $.

Published on 31 Mar 2021 - 21:23

score 63 · Answer 11 · 2026-03-26 12:38:29

63

Views

Intuitive implication of the fact that dual of $L_{p}$-norm space is $L_{q}$-norm space where $\frac{1}{p}+\frac{1}{q}=1$.

Published on 26 Mar 2026 - 12:38

score 250 · Answer 12 · 2021-04-10 12:30:54

250

Views

Corollary Hölder's inequality: $\Vert f \Vert_p=\sup_{\{g\::\:\Vert g\Vert _q=1\}}\int fg$

Published on 10 Apr 2021 - 12:30

score 38 · Answer 13 · 2026-02-24 08:41:11

38

Views

Holder-type inequality or not (optimal transport in Riemannian manifolds)?

Published on 24 Feb 2026 - 8:41

score 528 · Answer 14 · 2021-04-21 17:02:20

528

Views

Hölder's inequality with $p=1,q=\infty$ and SDEs

Published on 21 Apr 2021 - 17:02

score 29 · Answer 15 · 2021-04-22 15:47:38

29

Views

Seemingly Simple Probabilistic Inequality Question

Published on 22 Apr 2021 - 15:47

List Question

$f, g$ measurable, $\lVert g\rVert_1=1$ and $0 \le a \le f \le b$ so $\int_{\mathbb{R^n}} \frac{g}{f}dx \ge \frac{1}{\int_{\mathbb{R^n}} fg dx}$

Algebraic inequality $\sum \frac{x^3}{(x+y)(x+z)(x+t)}\geq \frac{1}{2}$

Let $f, g :(0,1) \to \mathbb{R}\,\,$ s.t. $\lVert g \rVert_2 =3$ and $\lVert f \rVert_1 = e\,\,$, show that $|\int_{0}^{1} g \sqrt{\log(f)}dx| \le 3$

Kind of equality on the sphere in Holder inequality

An interpolation inequality using Holder inequality

$\sum\sqrt{\frac{2a}{b+c}}\le\sqrt[3]{9\sum\frac{a}{b}}$

$f^{p_1}$ belongs to $L^p(E)$ and $g = \chi_{E}$ belongs to $L^q(E)$?

Vectorial $L^p$ spaces

Application of Hölder's inequality: $(a+b)^t \le 2^t(a^t+b^t)$ for $t\ge 1.$

Prove that $\cup_{1<p\leq\infty} L^p([0,1])\subset L^1([0,1]) $.

Intuitive implication of the fact that dual of $L_{p}$-norm space is $L_{q}$-norm space where $\frac{1}{p}+\frac{1}{q}=1$.

Corollary Hölder's inequality: $\Vert f \Vert_p=\sup_{\{g\::\:\Vert g\Vert _q=1\}}\int fg$

Holder-type inequality or not (optimal transport in Riemannian manifolds)?

Hölder's inequality with $p=1,q=\infty$ and SDEs

Seemingly Simple Probabilistic Inequality Question

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