Question

Prove that $ \lim _{a \rightarrow 0}\left\|T_{a} f-f\right\|_{L^{1}}=0 . $

score 37 · Answer 1 · 2026-04-17 13:44:53

37

Views

Prove that $ \lim _{a \rightarrow 0}\left\|T_{a} f-f\right\|_{L^{1}}=0 . $

Published on 17 Apr 2026 - 13:44

score 76 · Answer 2 · 2026-04-13 19:06:03

76

Views

The seminorm of $L^{p,\infty}$ does not fulfill the triangular inequality.

Published on 13 Apr 2026 - 19:06

score 57 · Answer 3 · 2026-04-16 01:16:15

57

Views

The dual space $L_\infty(\mathbb{R})$ can't be identified with $L_1(\mathbb{R})$

Published on 16 Apr 2026 - 1:16

score 83 · Answer 4 · 2026-04-12 01:12:38

83

Views

Compact spaces in $l_p$ with $(1\leq p<+\infty)$

Published on 12 Apr 2026 - 1:12

score 146 · Answer 5 · 2026-04-16 18:06:48

146

Views

For $u \in L^2([0,T])$ there exists $u_m \in C^\infty$ such that $u_m \to u$ in $L^2_{loc}(]0,T[)$.

Published on 16 Apr 2026 - 18:06

score 170 · Answer 6 · 2026-04-16 03:37:14

170

Views

bounded convergence in $L^2$ and $\mathcal{D}'$

Published on 16 Apr 2026 - 3:37

score 57 · Answer 7 · 2026-04-17 13:10:17

57

Views

What is required in order to prove $||\cdot||_{\infty}$ is well defined (for ($L^\infty, ||\cdot||_{\infty}$)

Published on 17 Apr 2026 - 13:10

score 282 · Answer 8 · 2026-04-30 04:09:26

282

Views

Proof of a weighted norm inequality.

Published on 30 Apr 2026 - 4:09

score 118 · Answer 9 · 2026-04-11 17:05:47

118

Views

Spectrum of positive linear operators defined for every $L^p$ space.

Published on 11 Apr 2026 - 17:05

score 137 · Answer 10 · 2026-04-30 05:15:47

137

Views

$(\int_{\mathbb{R}}|\int_\mathbb{R}{\mathcal{F}^{-1}}(\chi_{(t,\infty)}\hat{f})(\xi)m'(t)dt|^pd\xi)^{1/p}\leq C_p\|m'\|_{L^1}\|f\|_{L^p}$

Published on 30 Apr 2026 - 5:15

score 332 · Answer 11 · 2026-04-15 07:39:40

332

Views

Proof that dual of $L^p$ is $L^q$

Published on 15 Apr 2026 - 7:39

score 80 · Answer 12 · 2026-04-17 07:54:34

80

Views

Show that $\mathcal Y \subset C([0,T], X_1)$ continuously.

Published on 17 Apr 2026 - 7:54

score 37 · Answer 13 · 2026-04-14 16:25:51

37

Views

The limit of an orthonormal system in $L^2([0,1])$

Published on 14 Apr 2026 - 16:25

score 101 · Answer 14 · 2026-04-17 09:50:39

101

Views

Prove that the $L^p$ and $L^q$ norms are equivalent on a closed subspace $X$ of $L^p(\mu) \cap L^q(\mu)$

Published on 17 Apr 2026 - 9:50

score 251 · Answer 15 · 2026-04-10 04:43:51

251

Views

Folland theorem 6.19 proof doubt

Published on 10 Apr 2026 - 4:43

List Question

Prove that $ \lim _{a \rightarrow 0}\left\|T_{a} f-f\right\|_{L^{1}}=0 . $

The seminorm of $L^{p,\infty}$ does not fulfill the triangular inequality.

The dual space $L_\infty(\mathbb{R})$ can't be identified with $L_1(\mathbb{R})$

Compact spaces in $l_p$ with $(1\leq p<+\infty)$

For $u \in L^2([0,T])$ there exists $u_m \in C^\infty$ such that $u_m \to u$ in $L^2_{loc}(]0,T[)$.

bounded convergence in $L^2$ and $\mathcal{D}'$

What is required in order to prove $||\cdot||_{\infty}$ is well defined (for ($L^\infty, ||\cdot||_{\infty}$)

Proof of a weighted norm inequality.

Spectrum of positive linear operators defined for every $L^p$ space.

$(\int_{\mathbb{R}}|\int_\mathbb{R}{\mathcal{F}^{-1}}(\chi_{(t,\infty)}\hat{f})(\xi)m'(t)dt|^pd\xi)^{1/p}\leq C_p\|m'\|_{L^1}\|f\|_{L^p}$

Proof that dual of $L^p$ is $L^q$

Show that $\mathcal Y \subset C([0,T], X_1)$ continuously.

The limit of an orthonormal system in $L^2([0,1])$

Prove that the $L^p$ and $L^q$ norms are equivalent on a closed subspace $X$ of $L^p(\mu) \cap L^q(\mu)$

Folland theorem 6.19 proof doubt

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