Question

$|X|\in\mathcal{L}^p\Leftrightarrow X\in\mathcal{L}^p\hspace{0.3cm}\forall p>1$?

score 45 · Answer 1 · 2020-06-06 10:46:23

45

Views

$|X|\in\mathcal{L}^p\Leftrightarrow X\in\mathcal{L}^p\hspace{0.3cm}\forall p>1$?

Published on 06 Jun 2020 - 10:46

score 357 · Answer 2 · 2020-06-07 09:59:10

357

Views

Weak-* convergence in $L^{\infty}$ implies weak convergence in $L^p$ on bounded set

Published on 07 Jun 2020 - 9:59

score 65 · Answer 3 · 2020-06-08 19:27:29

65

Views

Linear Functional is Discontinuous

Published on 08 Jun 2020 - 19:27

score 100 · Answer 4 · 2020-06-08 21:36:38

100

Views

Let $p \in (1, \infty)$. If $f \in L^p(\mathbb{R})$ then $\lim_{x \rightarrow \infty} \int_{x}^{x+1}f(x)dx=0$

Published on 08 Jun 2020 - 21:36

score 37 · Answer 5 · 2020-06-09 23:24:38

37

Views

Convergence of a sequence of linear bounded operators in $L_2(B(0,1))$

Published on 09 Jun 2020 - 23:24

score 112 · Answer 6 · 2020-06-10 17:16:15

112

Views

Dose convergence in integral and measure imply convergence in L

Published on 10 Jun 2020 - 17:16

score 118 · Answer 7 · 2020-06-10 22:14:03

118

Views

Prove the weak convergence of a sequence of convolutions in $L^r$

Published on 10 Jun 2020 - 22:14

score 279 · Answer 8 · 2026-03-30 03:38:26

279

Views

Find the spectrum of a linear bounded operator $T:L^1([0,1]) \longrightarrow L^1([0,1])$

Published on 30 Mar 2026 - 3:38

score 243 · Answer 9 · 2020-06-13 12:21:54

243

Views

Special case of Riesz-Thorin Interpolation Theorem $L^{p_0} \cap L^{p_1} \to L^1$

Published on 13 Jun 2020 - 12:21

score 27 · Answer 10 · 2020-06-13 15:56:52

27

Views

For which $p \in (0,\infty)$ is $\int_{y=1}^{\infty}\int_{x=1}^{x=\sqrt{y}}|\cos x\sin y |^p\frac{1}{y2}dxdy<\infty$

Published on 13 Jun 2020 - 15:56

score 238 · Answer 11 · 2026-04-04 09:41:23

238

Views

For the proof that $L^p$, $p≠2$, is not a Hilbert space, why the parallelogram law is violated?

Published on 04 Apr 2026 - 9:41

score 45 · Answer 12 · 2020-06-14 12:46:58

45

Views

IF $f\in L^1[0,1]$ satisfies $\int_0^1 fg^{(n)}dx=0$ for all smooth $g$ supported in $(0,1)$ then $f$ is a polynomial of degree $\leq n-1$.

Published on 14 Jun 2020 - 12:46

score 59 · Answer 13 · 2020-06-16 08:32:20

59

Views

Norm of functional on $L^4[0, 1]$

Published on 16 Jun 2020 - 8:32

score 317 · Answer 14 · 2026-04-03 05:18:05

317

Views

Why $C^{\infty}(\Omega) \cap W^{1, \infty}(\Omega)$ isn't dense in $W^{1, \infty}(\Omega)$?

Published on 03 Apr 2026 - 5:18

score 188 · Answer 15 · 2026-03-25 17:38:41

188

Views

Lp spaces and Hölder Inequality

Published on 25 Mar 2026 - 17:38

List Question

$|X|\in\mathcal{L}^p\Leftrightarrow X\in\mathcal{L}^p\hspace{0.3cm}\forall p>1$?

Weak-* convergence in $L^{\infty}$ implies weak convergence in $L^p$ on bounded set

Linear Functional is Discontinuous

Let $p \in (1, \infty)$. If $f \in L^p(\mathbb{R})$ then $\lim_{x \rightarrow \infty} \int_{x}^{x+1}f(x)dx=0$

Convergence of a sequence of linear bounded operators in $L_2(B(0,1))$

Dose convergence in integral and measure imply convergence in L

Prove the weak convergence of a sequence of convolutions in $L^r$

Find the spectrum of a linear bounded operator $T:L^1([0,1]) \longrightarrow L^1([0,1])$

Special case of Riesz-Thorin Interpolation Theorem $L^{p_0} \cap L^{p_1} \to L^1$

For which $p \in (0,\infty)$ is $\int_{y=1}^{\infty}\int_{x=1}^{x=\sqrt{y}}|\cos x\sin y |^p\frac{1}{y2}dxdy<\infty$

For the proof that $L^p$, $p≠2$, is not a Hilbert space, why the parallelogram law is violated?

IF $f\in L^1[0,1]$ satisfies $\int_0^1 fg^{(n)}dx=0$ for all smooth $g$ supported in $(0,1)$ then $f$ is a polynomial of degree $\leq n-1$.

Norm of functional on $L^4[0, 1]$

Why $C^{\infty}(\Omega) \cap W^{1, \infty}(\Omega)$ isn't dense in $W^{1, \infty}(\Omega)$?

Lp spaces and Hölder Inequality

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