Question

Simple bound for $L^p$ norm

score 176 · Answer 1 · 2026-03-28 02:42:39

176

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Simple bound for $L^p$ norm

Published on 28 Mar 2026 - 2:42

score 50 · Answer 2 · 2019-01-03 08:04:46

50

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Show that $\phi(r) = ||f||_{L^r(0,1)}$, $r\in [1,2]$ is continuous function of r.

Published on 03 Jan 2019 - 8:04

score 285 · Answer 3 · 2026-03-28 03:55:28

285

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Given that $f \in L^2(\mathbb{T})$ and the sequence of Fourier coefficients $(\hat{f_n})\in l^1(\mathbb{Z})$, must $f$ be continuous?

Published on 28 Mar 2026 - 3:55

score 33 · Answer 4 · 2019-01-05 13:56:33

33

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$f \in C_{00}(\mathbb{R^p},\mathbb{C})$. $ \mapsto f_t \in L_\infty(\mathbb{R}^p, \mathcal B_p, \lambda_p, \mathbb{C})$ uniformly continuous?

Published on 05 Jan 2019 - 13:56

score 92 · Answer 5 · 2026-03-25 04:53:19

92

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Interchanging limit and integral.

Published on 25 Mar 2026 - 4:53

score 224 · Answer 6 · 2026-03-25 16:08:19

224

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Dual space of $L^p(\Omega,\mathcal{A},\mu,\mathbb{R}^d)$.

Published on 25 Mar 2026 - 16:08

score 189 · Answer 7 · 2026-02-23 01:05:34

189

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Banach algebra $l^p$ is not isomorphic to $C^{*}$ algebra

Published on 23 Feb 2026 - 1:05

score 548 · Answer 8 · 2026-03-28 16:56:52

548

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What is the operator norm of $Tf(x) = x^2f(x)$?

Published on 28 Mar 2026 - 16:56

score 115 · Answer 9 · 2019-01-07 20:21:20

115

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Brezis exercise, under what condition does $f$ belongs to $L_p(\mathbb{R^n})$

Published on 07 Jan 2019 - 20:21

score 106 · Answer 10 · 2019-01-07 21:54:17

106

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Brezis excercise 4.3.1. If $f$ and $g$ are in $L^p(\Omega)$, then $h = max\{f(x),g(x)\}$ is in $L_p(\Omega)$.

Published on 07 Jan 2019 - 21:54

score 23 · Answer 11 · 2026-03-25 20:17:04

23

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$C_0(\Delta(l^p))$ description

Published on 25 Mar 2026 - 20:17

score 43 · Answer 12 · 2026-03-28 17:04:42

43

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analysis of $T : f \to Tf$ with $[T(f)](x) = ie^{i\pi x}(\int_0^x e^{-i\pi t}f(t)dt - \int_x^1 e^{-i\pi t}f(t)dt)$

Published on 28 Mar 2026 - 17:04

score 71 · Answer 13 · 2019-01-08 14:13:11

71

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For which $p \in [1,\infty]$ does $g, g_{A}$ and $g_{A^{c}} \in \mathcal{L}^p$ hold?

Published on 08 Jan 2019 - 14:13

score 214 · Answer 14 · 2019-01-09 19:36:39

214

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Excercise 4.3 (3) in Brezis. Convergence in $L_p$

Published on 09 Jan 2019 - 19:36

score 183 · Answer 15 · 2019-01-10 18:42:13

183

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Brezis excercise 4.12: $L_p$ is uniformly convex for $1<p\leq 2$

Published on 10 Jan 2019 - 18:42

List Question

Simple bound for $L^p$ norm

Show that $\phi(r) = ||f||_{L^r(0,1)}$, $r\in [1,2]$ is continuous function of r.

Given that $f \in L^2(\mathbb{T})$ and the sequence of Fourier coefficients $(\hat{f_n})\in l^1(\mathbb{Z})$, must $f$ be continuous?

$f \in C_{00}(\mathbb{R^p},\mathbb{C})$. $ \mapsto f_t \in L_\infty(\mathbb{R}^p, \mathcal B_p, \lambda_p, \mathbb{C})$ uniformly continuous?

Interchanging limit and integral.

Dual space of $L^p(\Omega,\mathcal{A},\mu,\mathbb{R}^d)$.

Banach algebra $l^p$ is not isomorphic to $C^{*}$ algebra

What is the operator norm of $Tf(x) = x^2f(x)$?

Brezis exercise, under what condition does $f$ belongs to $L_p(\mathbb{R^n})$

Brezis excercise 4.3.1. If $f$ and $g$ are in $L^p(\Omega)$, then $h = max\{f(x),g(x)\}$ is in $L_p(\Omega)$.

$C_0(\Delta(l^p))$ description

analysis of $T : f \to Tf$ with $[T(f)](x) = ie^{i\pi x}(\int_0^x e^{-i\pi t}f(t)dt - \int_x^1 e^{-i\pi t}f(t)dt)$

For which $p \in [1,\infty]$ does $g, g_{A}$ and $g_{A^{c}} \in \mathcal{L}^p$ hold?

Excercise 4.3 (3) in Brezis. Convergence in $L_p$

Brezis excercise 4.12: $L_p$ is uniformly convex for $1<p\leq 2$

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