Question

Brezis' exercise 6.18.3: prove that $\sigma\left(S_r\right)=[-1,1]$

score 54 · Answer 1 · 2026-04-01 11:59:11

54

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Brezis' exercise 6.18.3: prove that $\sigma\left(S_r\right)=[-1,1]$

Published on 01 Apr 2026 - 11:59

score 47 · Answer 2 · 2026-04-01 12:06:29

47

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Brezis' exercise 6.18.5: prove that $\sigma(S_{\ell})=[-1,1]$

Published on 01 Apr 2026 - 12:06

score 96 · Answer 3 · 2026-04-01 12:05:10

96

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Let $x_{n+1} := \frac{x_n-y_{n+1}}{\lambda}$ for $n \ge 1$. Can we prove that $|x|_2 < \infty$?

Published on 01 Apr 2026 - 12:05

score 90 · Answer 4 · 2026-04-11 03:35:48

90

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Weighted L infinity norm

Published on 11 Apr 2026 - 3:35

score 70 · Answer 5 · 2026-04-11 02:59:48

70

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Limits using layer-cake representations for $L^p$ space involving two functions

Published on 11 Apr 2026 - 2:59

score 84 · Answer 6 · 2026-03-27 03:49:44

84

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$L^1$ equicontinuity for functions with uniformly bounded total variation

Published on 27 Mar 2026 - 3:49

score 96 · Answer 7 · 2023-07-07 21:48:45

96

Views

"Proving" $L^q \subseteq L^p$ for any $p <\infty$.

Published on 07 Jul 2023 - 21:48

score 86 · Answer 8 · 2023-07-08 13:37:15

86

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If $\Vert f \Vert_p < \infty$ for some $1 < p < \infty$ prove that $\lim_{t\to \infty} t^{-(1-1/p)} \int_0^t f(x) \, dx =0$.

Published on 08 Jul 2023 - 13:37

score 39 · Answer 9 · 2026-04-07 22:59:42

39

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Brezis' exercise 6.18.8: prove that the spaces $R(S_r \pm I)$ and $R(S_{\ell} \pm I)$ are dense and that they are not closed

Published on 07 Apr 2026 - 22:59

score 35 · Answer 10 · 2026-04-07 22:56:53

35

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Brezis' exercise 6.18.9: determine $E V (S_r \circ M)$

Published on 07 Apr 2026 - 22:56

score 189 · Answer 11 · 2023-07-10 15:37:27

189

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Application of Fubini's Theorem - showing an integral-defined operator on $L^p$ outputs measurable functions

Published on 10 Jul 2023 - 15:37

score 79 · Answer 12 · 2026-03-26 09:51:24

79

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If $f_n \rightarrow f$ weakly in $L^p$, then $\sqrt{f_n} \rightarrow \sqrt{f}$ weakly in $L^{2p}$?

Published on 26 Mar 2026 - 9:51

score 38 · Answer 13 · 2023-07-11 09:59:22

38

Views

Element in Lp Vs Lp-Bounded

Published on 11 Jul 2023 - 9:59

score 50 · Answer 14 · 2026-03-26 05:56:00

50

Views

Inequality in the unit ball of Sobolev Space $W^{1,1}(\mathbb{R})$

Published on 26 Mar 2026 - 5:56

score 148 · Answer 15 · 2026-04-01 13:34:06

148

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Brezis' exercise 6.18.10: how to prove that $\sigma (S_r \circ M)=[-|\alpha|, |\alpha|]$ in case $\alpha \neq 0$?

Published on 01 Apr 2026 - 13:34

List Question

Brezis' exercise 6.18.3: prove that $\sigma\left(S_r\right)=[-1,1]$

Brezis' exercise 6.18.5: prove that $\sigma(S_{\ell})=[-1,1]$

Let $x_{n+1} := \frac{x_n-y_{n+1}}{\lambda}$ for $n \ge 1$. Can we prove that $|x|_2 < \infty$?

Weighted L infinity norm

Limits using layer-cake representations for $L^p$ space involving two functions

$L^1$ equicontinuity for functions with uniformly bounded total variation

"Proving" $L^q \subseteq L^p$ for any $p <\infty$.

If $\Vert f \Vert_p < \infty$ for some $1 < p < \infty$ prove that $\lim_{t\to \infty} t^{-(1-1/p)} \int_0^t f(x) \, dx =0$.

Brezis' exercise 6.18.8: prove that the spaces $R(S_r \pm I)$ and $R(S_{\ell} \pm I)$ are dense and that they are not closed

Brezis' exercise 6.18.9: determine $E V (S_r \circ M)$

Application of Fubini's Theorem - showing an integral-defined operator on $L^p$ outputs measurable functions

If $f_n \rightarrow f$ weakly in $L^p$, then $\sqrt{f_n} \rightarrow \sqrt{f}$ weakly in $L^{2p}$?

Element in Lp Vs Lp-Bounded

Inequality in the unit ball of Sobolev Space $W^{1,1}(\mathbb{R})$

Brezis' exercise 6.18.10: how to prove that $\sigma (S_r \circ M)=[-|\alpha|, |\alpha|]$ in case $\alpha \neq 0$?

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