Question

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

score 518 · Answer 1 · 2026-04-13 06:53:17

518

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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 13 Apr 2026 - 6:53

score 78 · Answer 2 · 2026-04-18 08:56:44

78

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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 18 Apr 2026 - 8:56

score 319 · Answer 3 · 2026-04-11 23:03:21

319

Views

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

Published on 11 Apr 2026 - 23:03

score 171 · Answer 4 · 2026-04-12 04:57:31

171

Views

$L^2$-valued integral as parameter integral

Published on 12 Apr 2026 - 4:57

score 132 · Answer 5 · 2026-05-10 18:04:21

132

Views

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

Published on 10 May 2026 - 18:04

score 99 · Answer 6 · 2026-04-13 18:31:00

99

Views

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

Published on 13 Apr 2026 - 18:31

score 459 · Answer 7 · 2026-04-15 23:23:16

459

Views

Prove Lp ball closed in L1

Published on 15 Apr 2026 - 23:23

score 1.3k · Answer 8 · 2026-04-16 15:17:28

1.3k

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

Published on 16 Apr 2026 - 15:17

score 283 · Answer 9 · 2026-05-10 18:58:11

283

Views

L2 inequality implies completeness

Published on 10 May 2026 - 18:58

score 105 · Answer 10 · 2026-04-12 09:58:08

105

Views

Estimates in Lp and Sobolev spaces

Published on 12 Apr 2026 - 9:58

score 117 · Answer 11 · 2026-05-11 02:45:35

117

Views

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

Published on 11 May 2026 - 2:45

score 56 · Answer 12 · 2026-04-15 16:47:01

56

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 15 Apr 2026 - 16:47

score 75 · Answer 13 · 2026-05-06 19:04:07

75

Views

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

Published on 06 May 2026 - 19:04

score 247 · Answer 14 · 2026-04-16 15:58:46

247

Views

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

Published on 16 Apr 2026 - 15:58

score 48 · Answer 15 · 2026-04-16 06:58:21

48

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 16 Apr 2026 - 6:58

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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