Question

What assumptions on $f$ guarantee that $\sup_{|u|\le r} g(u)\in L^{\infty}(\mathbb{R})$?

score 79 · Answer 1 · 2026-04-13 16:06:14

79

Views

What assumptions on $f$ guarantee that $\sup_{|u|\le r} g(u)\in L^{\infty}(\mathbb{R})$?

Published on 13 Apr 2026 - 16:06

score 35 · Answer 2 · 2026-04-15 09:57:17

35

Views

How to show that $UM_{\phi\circ f} U^{-1} = M_{\phi\circ f}$ for bounded measurable function $\phi$

Published on 15 Apr 2026 - 9:57

score 77 · Answer 3 · 2026-04-15 19:07:52

77

Views

proving $L^p$ as a normed vector space for $p > 1$.

Published on 15 Apr 2026 - 19:07

score 32 · Answer 4 · 2026-04-16 01:07:57

32

Views

If $f:\Bbb{R}\to\Bbb{R}$ is continuous and $|f(x)|\leq a+b|x|^\alpha$, then the induced map $f:L^p\to L^{p/\alpha}$ is continuous?

Published on 16 Apr 2026 - 1:07

score 70 · Answer 5 · 2026-04-12 22:42:38

70

Views

$l^{p}$ and $L^{p}$ applications in PDEs

Published on 12 Apr 2026 - 22:42

score 102 · Answer 6 · 2026-04-12 03:13:52

102

Views

Inequality for $l^p$-norm

Published on 12 Apr 2026 - 3:13

score 51 · Answer 7 · 2026-04-12 10:29:24

51

Views

Dual of p-integrable functions

Published on 12 Apr 2026 - 10:29

score 54 · Answer 8 · 2026-04-12 03:20:09

54

Views

When the image of operator be subset of $l_p$

Published on 12 Apr 2026 - 3:20

score 86 · Answer 9 · 2026-04-13 07:31:36

86

Views

$\hat{L^p}\subseteq L^p$

Published on 13 Apr 2026 - 7:31

score 59 · Answer 10 · 2026-04-10 18:41:53

59

Views

Necessary condition for integrability of positive measurable function over unbounded domain

Published on 10 Apr 2026 - 18:41

score 69 · Answer 11 · 2026-04-15 23:18:22

69

Views

Proof that $f_{n} = \chi_{\Omega_{n}}f \to f$ in $L^{2}$

Published on 15 Apr 2026 - 23:18

score 326 · Answer 12 · 2026-04-28 17:52:11

326

Views

Assume $f,g, fg\in L^1(\mathbb{R}^n)$ and $\widehat{f}\in L^1(\mathbb{R}^n)$. Prove that $\widehat{fg}=(2\pi)^{-n}\widehat{f}*\widehat{g}$

Published on 28 Apr 2026 - 17:52

score 53 · Answer 13 · 2026-04-14 08:45:31

53

Views

If $f\in\mathcal{S}$, then the functions $\frac{\partial f}{\partial x_j}$ and $x_jf$ are in $\mathcal{S}$

Published on 14 Apr 2026 - 8:45

score 25 · Answer 14 · 2026-04-15 10:07:49

25

Views

inequality using propagation function $w$.

Published on 15 Apr 2026 - 10:07

score 89 · Answer 15 · 2026-04-16 00:59:26

89

Views

Determine the norm $\|\phi\|,$ where $~~\phi \in l_p^*$.

Published on 16 Apr 2026 - 0:59

List Question

What assumptions on $f$ guarantee that $\sup_{|u|\le r} g(u)\in L^{\infty}(\mathbb{R})$?

How to show that $UM_{\phi\circ f} U^{-1} = M_{\phi\circ f}$ for bounded measurable function $\phi$

proving $L^p$ as a normed vector space for $p > 1$.

If $f:\Bbb{R}\to\Bbb{R}$ is continuous and $|f(x)|\leq a+b|x|^\alpha$, then the induced map $f:L^p\to L^{p/\alpha}$ is continuous?

$l^{p}$ and $L^{p}$ applications in PDEs

Inequality for $l^p$-norm

Dual of p-integrable functions

When the image of operator be subset of $l_p$

$\hat{L^p}\subseteq L^p$

Necessary condition for integrability of positive measurable function over unbounded domain

Proof that $f_{n} = \chi_{\Omega_{n}}f \to f$ in $L^{2}$

Assume $f,g, fg\in L^1(\mathbb{R}^n)$ and $\widehat{f}\in L^1(\mathbb{R}^n)$. Prove that $\widehat{fg}=(2\pi)^{-n}\widehat{f}*\widehat{g}$

If $f\in\mathcal{S}$, then the functions $\frac{\partial f}{\partial x_j}$ and $x_jf$ are in $\mathcal{S}$

inequality using propagation function $w$.

Determine the norm $\|\phi\|,$ where $~~\phi \in l_p^*$.

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