Question

Linear operator on sequences $M_y$ given by $M_y(x) = (y_jx_j)_{j \in \mathbb{N}}$ preserves $l^p$ iff $y \in l^{\infty}$

score 50 · Answer 1 · 2026-04-14 10:13:24

50

Views

Linear operator on sequences $M_y$ given by $M_y(x) = (y_jx_j)_{j \in \mathbb{N}}$ preserves $l^p$ iff $y \in l^{\infty}$

Published on 14 Apr 2026 - 10:13

score 197 · Answer 2 · 2026-04-15 10:26:39

197

Views

$L^q(X,\mu)\subset L^p(X,\mu)\iff X$ does not contain sets of arbitrarily large measure

Published on 15 Apr 2026 - 10:26

score 86 · Answer 3 · 2026-04-10 02:40:07

86

Views

Notation for Lp spaces

Published on 10 Apr 2026 - 2:40

score 39 · Answer 4 · 2026-04-13 15:26:16

39

Views

Show that $f=0$ almost everywhere

Published on 13 Apr 2026 - 15:26

score 201 · Answer 5 · 2026-05-15 05:26:18

201

Views

Boundedness + convergence in $L^2_{\text{loc}}$ implies weak convergence?

Published on 15 May 2026 - 5:26

score 41 · Answer 6 · 2026-04-12 19:46:22

41

Views

Convergence in $L^p$: A simply question about Dominated Convergence Theorem and a doubt on the limit of intersection.

Published on 12 Apr 2026 - 19:46

score 125 · Answer 7 · 2026-04-16 12:26:06

125

Views

$L^{p}$ convergence equivalent condition

Published on 16 Apr 2026 - 12:26

score 44 · Answer 8 · 2026-05-15 05:27:29

44

Views

If $\int_\Omega (u_n/\delta)^2=1$ then $(u_n)_{n=1}^{\infty}$ is bounded in $H_{0}^{1}(\Omega)$

Published on 15 May 2026 - 5:27

score 78 · Answer 9 · 2026-04-14 03:44:46

78

Views

An exercise on weak convergence from Henrot's book

Published on 14 Apr 2026 - 3:44

score 54 · Answer 10 · 2026-04-12 22:42:27

54

Views

$L_1$ convergence implies a.s. convergence for a sequence that is monotonically decreasing in $n$?

Published on 12 Apr 2026 - 22:42

score 93 · Answer 11 · 2026-04-13 17:38:11

93

Views

Condition where $L_1$ convergence implies pointwise a.e. convergence, using Stein's Maximal Principle.

Published on 13 Apr 2026 - 17:38

score 49 · Answer 12 · 2026-04-15 07:48:35

49

Views

Convergence in $L^p(B_r(0)) \implies$ convergence in $L^p(\mathbb{R}^N)$?

Published on 15 Apr 2026 - 7:48

score 60 · Answer 13 · 2026-04-14 02:27:05

60

Views

Bounded function in $L_1([0,\infty))$ but not in $L_2([0,\infty))$

Published on 14 Apr 2026 - 2:27

score 49 · Answer 14 · 2026-04-17 06:03:24

49

Views

Inequality in $L^2$ space $(\|v\| + \|v'\|)(\|w\|+\|w'\|) \le \sqrt{2} (\|v\|^2+\|v'\|^2)^{1/2}\sqrt{2}(\|w\|^2+\|w'\|^2) ^{1/2}$?

Published on 17 Apr 2026 - 6:03

score 201 · Answer 15 · 2026-04-12 07:12:39

201

Views

$l^p$ spaces are increasing in $p$

Published on 12 Apr 2026 - 7:12

List Question

Linear operator on sequences $M_y$ given by $M_y(x) = (y_jx_j)_{j \in \mathbb{N}}$ preserves $l^p$ iff $y \in l^{\infty}$

$L^q(X,\mu)\subset L^p(X,\mu)\iff X$ does not contain sets of arbitrarily large measure

Notation for Lp spaces

Show that $f=0$ almost everywhere

Boundedness + convergence in $L^2_{\text{loc}}$ implies weak convergence?

Convergence in $L^p$: A simply question about Dominated Convergence Theorem and a doubt on the limit of intersection.

$L^{p}$ convergence equivalent condition

If $\int_\Omega (u_n/\delta)^2=1$ then $(u_n)_{n=1}^{\infty}$ is bounded in $H_{0}^{1}(\Omega)$

An exercise on weak convergence from Henrot's book

$L_1$ convergence implies a.s. convergence for a sequence that is monotonically decreasing in $n$?

Condition where $L_1$ convergence implies pointwise a.e. convergence, using Stein's Maximal Principle.

Convergence in $L^p(B_r(0)) \implies$ convergence in $L^p(\mathbb{R}^N)$?

Bounded function in $L_1([0,\infty))$ but not in $L_2([0,\infty))$

Inequality in $L^2$ space $(\|v\| + \|v'\|)(\|w\|+\|w'\|) \le \sqrt{2} (\|v\|^2+\|v'\|^2)^{1/2}\sqrt{2}(\|w\|^2+\|w'\|^2) ^{1/2}$?

$l^p$ spaces are increasing in $p$

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