Question

If $m(X)<\infty$ and $f$ bounded and measurable, then $1\leq q<p<\infty$ implies $\|f\|_{p}^{p}\leq\|f\|_{q}^{q}\|f\|_{\infty}^{p-q}.$

score 38 · Answer 1 · 2026-03-30 05:13:53

38

Views

If $m(X)<\infty$ and $f$ bounded and measurable, then $1\leq q<p<\infty$ implies $\|f\|_{p}^{p}\leq\|f\|_{q}^{q}\|f\|_{\infty}^{p-q}.$

Published on 30 Mar 2026 - 5:13

score 99 · Answer 2 · 2026-03-30 08:15:01

99

Views

Why chose $H^{-1}(\Omega)$ instead of $L^2(\Omega)$?

Published on 30 Mar 2026 - 8:15

score 114 · Answer 3 · 2026-03-25 08:12:44

114

Views

$L^p$ norm inequality for measurable function

Published on 25 Mar 2026 - 8:12

score 61 · Answer 4 · 2019-06-13 01:30:42

61

Views

Does $ \int_{\Omega} |f|g \mathrm{d} x \geq \| f \|_{L^1(\Omega)} (\operatorname{ess} \inf g) $ hold?

Published on 13 Jun 2019 - 1:30

score 138 · Answer 5 · 2026-03-25 08:13:38

138

Views

Trouble with Holder Inequality Gymnastics: $\left(\int fg^{q}\right)^{r-p}\leq\left(\int fg^p\right)^{r-q}\left(\int fg^r\right)^{q-p}.$

Published on 25 Mar 2026 - 8:13

score 173 · Answer 6 · 2019-06-14 19:18:18

173

Views

Properties of $L^2$ norm

Published on 14 Jun 2019 - 19:18

score 213 · Answer 7 · 2019-06-14 22:41:25

213

Views

Bartle 6.K elements of integration

Published on 14 Jun 2019 - 22:41

score 75 · Answer 8 · 2019-06-15 06:14:06

75

Views

Are these $ L^2 $ norms equivalent?

Published on 15 Jun 2019 - 6:14

score 25 · Answer 9 · 2019-06-15 21:21:25

25

Views

How to notate a function that's restricted to L² (or any space) in only some of its arguments?

Published on 15 Jun 2019 - 21:21

score 140 · Answer 10 · 2019-06-15 21:29:43

140

Views

What set $Y$ that $C_{c}(U) \subset Y$ and $Y$ separable w.r.t. $\vert \vert \cdot \vert \vert_{\infty}$

Published on 15 Jun 2019 - 21:29

score 86 · Answer 11 · 2019-06-16 10:57:15

86

Views

Triangle inequality in $L^p$

Published on 16 Jun 2019 - 10:57

score 106 · Answer 12 · 2019-06-17 08:08:07

106

Views

Tips on finding the correct upper bound for $\frac{1}{\vert x\vert(1+\vert x\vert)^d}$

Published on 17 Jun 2019 - 8:08

score 1.2k · Answer 13 · 2026-03-30 05:12:03

1.2k

Views

inverse triangle inequality in $L^p$

Published on 30 Mar 2026 - 5:12

score 154 · Answer 14 · 2026-03-30 05:15:28

154

Views

Riemann Lebesgues lemma in $L^p$

Published on 30 Mar 2026 - 5:15

score 50 · Answer 15 · 2019-06-17 17:39:25

50

Views

$f \in L^p ((0,1), \tan x\, dx)$

Published on 17 Jun 2019 - 17:39

List Question

If $m(X)<\infty$ and $f$ bounded and measurable, then $1\leq q<p<\infty$ implies $\|f\|_{p}^{p}\leq\|f\|_{q}^{q}\|f\|_{\infty}^{p-q}.$

Why chose $H^{-1}(\Omega)$ instead of $L^2(\Omega)$?

$L^p$ norm inequality for measurable function

Does $ \int_{\Omega} |f|g \mathrm{d} x \geq \| f \|_{L^1(\Omega)} (\operatorname{ess} \inf g) $ hold?

Trouble with Holder Inequality Gymnastics: $\left(\int fg^{q}\right)^{r-p}\leq\left(\int fg^p\right)^{r-q}\left(\int fg^r\right)^{q-p}.$

Properties of $L^2$ norm

Bartle 6.K elements of integration

Are these $ L^2 $ norms equivalent?

How to notate a function that's restricted to L² (or any space) in only some of its arguments?

What set $Y$ that $C_{c}(U) \subset Y$ and $Y$ separable w.r.t. $\vert \vert \cdot \vert \vert_{\infty}$

Triangle inequality in $L^p$

Tips on finding the correct upper bound for $\frac{1}{\vert x\vert(1+\vert x\vert)^d}$

inverse triangle inequality in $L^p$

Riemann Lebesgues lemma in $L^p$

$f \in L^p ((0,1), \tan x\, dx)$

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