Question

How can I show that the embedding of $W^{1,1}(a,b)$ in $C[a,b]$ is not compact?

score 515 · Answer 1 · 2018-05-17 11:08:47

515

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How can I show that the embedding of $W^{1,1}(a,b)$ in $C[a,b]$ is not compact?

Published on 17 May 2018 - 11:08

score 72 · Answer 2 · 2026-03-20 11:27:35

72

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Is $\int_{A_t} \frac{1}{|x_j|^{p}}\, dx \leq \sum_{j=1}^{d} \int_{A_{j,t}}\frac{1}{|x_j|^p}\, dx \leq \int_{A_t} \frac{1}{|x|^p} \,dx$?

Published on 20 Mar 2026 - 11:27

score 316 · Answer 3 · 2018-05-17 23:14:24

316

Views

Counting measure and inclusion of $\mathcal{L}_p$ spaces.

Published on 17 May 2018 - 23:14

score 168 · Answer 4 · 2018-05-18 16:05:35

168

Views

$L^2$-valued integral as parameter integral

Published on 18 May 2018 - 16:05

score 129 · Answer 5 · 2026-03-25 12:48:32

129

Views

Ergodic theory regarding positive contraction operators on $L^1$

Published on 25 Mar 2026 - 12:48

score 96 · Answer 6 · 2018-05-19 10:50:15

96

Views

Fourier transform of Fourier transform of $f \in L^1\cap L^2$

Published on 19 May 2018 - 10:50

score 456 · Answer 7 · 2018-05-20 03:10:18

456

Views

Prove Lp ball closed in L1

Published on 20 May 2018 - 3:10

score 1.3k · Answer 8 · 2018-05-20 09:00:15

1.3k

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$L^p$ norm convergence implies $L^p$ convergence

Published on 20 May 2018 - 9:00

score 279 · Answer 9 · 2026-03-25 13:32:54

279

Views

L2 inequality implies completeness

Published on 25 Mar 2026 - 13:32

score 102 · Answer 10 · 2018-05-21 14:52:42

102

Views

Estimates in Lp and Sobolev spaces

Published on 21 May 2018 - 14:52

score 113 · Answer 11 · 2018-05-21 18:31:40

113

Views

$||f||_p$ bounded by $\lim\inf ||f_n||_p$

Published on 21 May 2018 - 18:31

score 53 · Answer 12 · 2018-05-22 02:56:36

53

Views

Given $F(x) = \int_a^xf(t)dt$, for $f \in L^p([a,b])$, prove a uniform bound of $\sum_{i=0}^{n-1} \frac{|F(x_{i+1})-F(x_i)|^p}{(x_{i+1}-x_i)^{p-1}}$

Published on 22 May 2018 - 2:56

score 68 · Answer 13 · 2026-03-17 13:12:56

68

Views

$L^2$ convergence given weak $L^2$ convergence

Published on 17 Mar 2026 - 13:12

score 244 · Answer 14 · 2018-05-22 12:26:07

244

Views

If $X$ is a Banach space, is $\ell^{p}(X) \cong \ell^{q}(X^{*})$?

Published on 22 May 2018 - 12:26

score 45 · Answer 15 · 2018-05-22 13:43:16

45

Views

If $f \in L^{p}(0,\infty)$, $p \in [1, +\infty)$, find $\lim_{n \to \infty} \int_{0}^{\infty} \frac{\tan{\frac{\pi}{2(1+n^{p}x)}}}{n\ln{(1+x)}}f(x)dx$

Published on 22 May 2018 - 13:43

List Question

How can I show that the embedding of $W^{1,1}(a,b)$ in $C[a,b]$ is not compact?

Is $\int_{A_t} \frac{1}{|x_j|^{p}}\, dx \leq \sum_{j=1}^{d} \int_{A_{j,t}}\frac{1}{|x_j|^p}\, dx \leq \int_{A_t} \frac{1}{|x|^p} \,dx$?

Counting measure and inclusion of $\mathcal{L}_p$ spaces.

$L^2$-valued integral as parameter integral

Ergodic theory regarding positive contraction operators on $L^1$

Fourier transform of Fourier transform of $f \in L^1\cap L^2$

Prove Lp ball closed in L1

$L^p$ norm convergence implies $L^p$ convergence

L2 inequality implies completeness

Estimates in Lp and Sobolev spaces

$||f||_p$ bounded by $\lim\inf ||f_n||_p$

Given $F(x) = \int_a^xf(t)dt$, for $f \in L^p([a,b])$, prove a uniform bound of $\sum_{i=0}^{n-1} \frac{|F(x_{i+1})-F(x_i)|^p}{(x_{i+1}-x_i)^{p-1}}$

$L^2$ convergence given weak $L^2$ convergence

If $X$ is a Banach space, is $\ell^{p}(X) \cong \ell^{q}(X^{*})$?

If $f \in L^{p}(0,\infty)$, $p \in [1, +\infty)$, find $\lim_{n \to \infty} \int_{0}^{\infty} \frac{\tan{\frac{\pi}{2(1+n^{p}x)}}}{n\ln{(1+x)}}f(x)dx$

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