Question

How to show that $ \|f\|_\infty\leq m^{-\frac{1}{p}}\|f\|_p $ when every set of positive measure in $X$ has measure at least $m$?

score 154 · Answer 1 · 2026-04-16 12:52:38

154

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How to show that $ \|f\|_\infty\leq m^{-\frac{1}{p}}\|f\|_p $ when every set of positive measure in $X$ has measure at least $m$?

Published on 16 Apr 2026 - 12:52

score 106 · Answer 2 · 2026-04-13 18:15:10

106

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Understanding the proof of $l^p(A)\subset l^q(A)$ where $0<p<q\leq\infty$ in Folland's Real Analysis

Published on 13 Apr 2026 - 18:15

score 1.4k · Answer 3 · 2026-04-16 07:22:00

1.4k

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Space of continuous functions versus $L^\infty$

Published on 16 Apr 2026 - 7:22

score 1.5k · Answer 4 · 2026-04-15 21:43:22

1.5k

Views

Showing a generalized version of the Hölder inequality for $L^{p}$ spaces

Published on 15 Apr 2026 - 21:43

score 183 · Answer 5 · 2026-04-12 02:48:40

183

Views

Integrability of Rademacher Fourier series

Published on 12 Apr 2026 - 2:48

score 178 · Answer 6 · 2026-04-13 13:42:42

178

Views

Sequence spaces are isomorphic

Published on 13 Apr 2026 - 13:42

score 821 · Answer 7 · 2026-04-09 08:06:57

821

Views

Fejer's theorem for Fourier transforms of $L^1(\mathbb{R})$ functions

Published on 09 Apr 2026 - 8:06

score 212 · Answer 8 · 2026-04-17 14:23:29

212

Views

Boundedness of a sequence in the dual of $l^q$

Published on 17 Apr 2026 - 14:23

score 78 · Answer 9 · 2026-04-15 18:39:39

78

Views

Showing that $n^{-1/p}f(x/n) \rightharpoonup 0$ in $L^p(\mathbb{R})$

Published on 15 Apr 2026 - 18:39

score 186 · Answer 10 · 2026-04-16 09:48:49

186

Views

$\|f\|_\infty = \sup \{|f(x)| : x \in \mathbb R^n\}$

Published on 16 Apr 2026 - 9:48

score 146 · Answer 11 · 2026-04-17 11:01:48

146

Views

$L^p$ contraction of scalar conservation law solution

Published on 17 Apr 2026 - 11:01

score 31 · Answer 12 · 2026-04-13 16:21:33

31

Views

Show a set is othonormal in $L^2([a, a + T])$ - norm of a function composition?

Published on 13 Apr 2026 - 16:21

score 94 · Answer 13 · 2026-04-11 13:57:58

94

Views

Decomposition of a linear functional.

Published on 11 Apr 2026 - 13:57

score 200 · Answer 14 · 2026-04-13 21:25:06

200

Views

Extension map of $\ell^p$ in the term of $\ell^q$

Published on 13 Apr 2026 - 21:25

score 1.2k · Answer 15 · 2026-04-16 04:04:02

1.2k

Views

Sequence in $L^p([0,1])$ with no convergent subsequence

Published on 16 Apr 2026 - 4:04

List Question

How to show that $ \|f\|_\infty\leq m^{-\frac{1}{p}}\|f\|_p $ when every set of positive measure in $X$ has measure at least $m$?

Understanding the proof of $l^p(A)\subset l^q(A)$ where $0<p<q\leq\infty$ in Folland's Real Analysis

Space of continuous functions versus $L^\infty$

Showing a generalized version of the Hölder inequality for $L^{p}$ spaces

Integrability of Rademacher Fourier series

Sequence spaces are isomorphic

Fejer's theorem for Fourier transforms of $L^1(\mathbb{R})$ functions

Boundedness of a sequence in the dual of $l^q$

Showing that $n^{-1/p}f(x/n) \rightharpoonup 0$ in $L^p(\mathbb{R})$

$\|f\|_\infty = \sup \{|f(x)| : x \in \mathbb R^n\}$

$L^p$ contraction of scalar conservation law solution

Show a set is othonormal in $L^2([a, a + T])$ - norm of a function composition?

Decomposition of a linear functional.

Extension map of $\ell^p$ in the term of $\ell^q$

Sequence in $L^p([0,1])$ with no convergent subsequence

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