Question

Proving a theorem about weak convergence in $L^p$

score 43 · Answer 1 · 2026-04-12 07:55:54

43

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Proving a theorem about weak convergence in $L^p$

Published on 12 Apr 2026 - 7:55

score 25 · Answer 2 · 2024-01-15 23:05:02

25

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If $u\in L^\infty$, does the inequality $\int_\mathbb R u(x) |v(x)|^2 dx\le \|u\|_{L^\infty} \int_\mathbb R |v(x)|^2 dx$ hold true?

Published on 15 Jan 2024 - 23:05

score 63 · Answer 3 · 2026-04-12 00:47:49

63

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Proving that the absolute value function does not have second weak derivative

Published on 12 Apr 2026 - 0:47

score 77 · Answer 4 · 2026-04-08 20:46:10

77

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Reference request: $\ell^1$, $\ell^2$, $\ell^p$

Published on 08 Apr 2026 - 20:46

score 51 · Answer 5 · 2024-01-18 04:57:29

51

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Can the unit ball in $\ell^2$ be a countable union of rectangle set $\prod_{n\in\mathbb{N}}[a_n,b_n)$?

Published on 18 Jan 2024 - 4:57

score 44 · Answer 6 · 2026-04-12 14:32:37

44

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Finite measure subset of (possibly) infinite measure regarding $L^\infty$ norm

Published on 12 Apr 2026 - 14:32

score 47 · Answer 7 · 2026-03-29 19:07:43

47

Views

Interpolation spaces

Published on 29 Mar 2026 - 19:07

score 54 · Answer 8 · 2026-04-11 12:46:28

54

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Integration of discontinuous functions

Published on 11 Apr 2026 - 12:46

score 69 · Answer 9 · 2026-04-11 20:43:23

69

Views

For which $p\in [1,+\infty]$ is the following operator continuous?

Published on 11 Apr 2026 - 20:43

score 41 · Answer 10 · 2026-04-10 23:00:29

41

Views

Is there a way to express the geometric mean in terms of the $\mathrm{L}^p$ norms?

Published on 10 Apr 2026 - 23:00

score 110 · Answer 11 · 2026-03-26 12:35:10

110

Views

Lyapunov inequality and $L^p$ interpolation

Published on 26 Mar 2026 - 12:35

score 71 · Answer 12 · 2024-01-27 19:17:11

71

Views

Var$[X]$ exists if and only if $X\in L^2$

Published on 27 Jan 2024 - 19:17

score 91 · Answer 13 · 2026-04-12 13:50:17

91

Views

Continuous functions are weak*-dense in $L^\infty$

Published on 12 Apr 2026 - 13:50

score 27 · Answer 14 · 2024-02-01 16:39:20

27

Views

Convergence of composition of functions in $L^P$ spaces

Published on 01 Feb 2024 - 16:39

score 42 · Answer 15 · 2024-02-02 16:00:13

42

Views

Showing that the integral operator $Ku(x):=\int_{A}k(x,y)u(y)dy$ is a Hilbert-Schmidt operator if $k\in L^2(A^2)$ for $A\subset\mathbb{R}$

Published on 02 Feb 2024 - 16:00

List Question

Proving a theorem about weak convergence in $L^p$

If $u\in L^\infty$, does the inequality $\int_\mathbb R u(x) |v(x)|^2 dx\le \|u\|_{L^\infty} \int_\mathbb R |v(x)|^2 dx$ hold true?

Proving that the absolute value function does not have second weak derivative

Reference request: $\ell^1$, $\ell^2$, $\ell^p$

Can the unit ball in $\ell^2$ be a countable union of rectangle set $\prod_{n\in\mathbb{N}}[a_n,b_n)$?

Finite measure subset of (possibly) infinite measure regarding $L^\infty$ norm

Interpolation spaces

Integration of discontinuous functions

For which $p\in [1,+\infty]$ is the following operator continuous?

Is there a way to express the geometric mean in terms of the $\mathrm{L}^p$ norms?

Lyapunov inequality and $L^p$ interpolation

Var$[X]$ exists if and only if $X\in L^2$

Continuous functions are weak*-dense in $L^\infty$

Convergence of composition of functions in $L^P$ spaces

Showing that the integral operator $Ku(x):=\int_{A}k(x,y)u(y)dy$ is a Hilbert-Schmidt operator if $k\in L^2(A^2)$ for $A\subset\mathbb{R}$

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