Question

Is every bounded function in $L^p$ for any $p \ge 1$?

score 594 · Answer 1 · 2026-04-13 06:28:52

594

Views

Is every bounded function in $L^p$ for any $p \ge 1$?

Published on 13 Apr 2026 - 6:28

score 83 · Answer 2 · 2026-04-17 11:01:46

83

Views

$L^0( \mathbb P | \mathcal F_0 ; || \cdot ||_{\mathbb R^d} ) \subset L^0( \mathbb P | \mathcal F_1 ; || \cdot ||_{\mathbb R^d} ) $?

Published on 17 Apr 2026 - 11:01

score 56 · Answer 3 · 2026-04-16 05:05:00

56

Views

Seemingly simple inequality between $L_p$ norms (When is $\|f\|_p \leq \|f\|_2$?)

Published on 16 Apr 2026 - 5:05

score 86 · Answer 4 · 2026-04-14 20:22:54

86

Views

Continuity in the mean: $\lim_{y \to 0}\int_{\mathbb{R}^d}|f(x+y)-f(x)|dx=0$

Published on 14 Apr 2026 - 20:22

score 114 · Answer 5 · 2026-04-12 00:06:07

114

Views

Examples of $L^p \cap L^1$ convergence

Published on 12 Apr 2026 - 0:06

score 46 · Answer 6 · 2026-04-16 09:53:04

46

Views

Study the convergence of this sequence in $L^{2}(\mathbb{R})$

Published on 16 Apr 2026 - 9:53

score 131 · Answer 7 · 2026-03-25 12:50:07

131

Views

How can we show $\left\|g\ast f\right\|_{L^p}\le\left\|g\right\|_{L^1}\left\|f\right\|_{L^p}$?

Published on 25 Mar 2026 - 12:50

score 26 · Answer 8 · 2026-04-14 21:18:27

26

Views

How to prove this function is $L^{r}(E)$

Published on 14 Apr 2026 - 21:18

score 307 · Answer 9 · 2026-04-15 17:25:45

307

Views

Q: Exercise 6.R Bartle

Published on 15 Apr 2026 - 17:25

score 360 · Answer 10 · 2026-04-14 02:33:17

360

Views

Can the limit of a sequence of functions in $L_p$ and the limit in almost everywhere convergence be different?

Published on 14 Apr 2026 - 2:33

score 320 · Answer 11 · 2026-04-16 13:22:01

320

Views

Weak* convergence in $L^\infty$ and the strong convergence in $L^2$ of a mollification?

Published on 16 Apr 2026 - 13:22

score 453 · Answer 12 · 2026-04-15 06:57:04

453

Views

Relations between Bochner spaces $L^p(0,T;L^q)$

Published on 15 Apr 2026 - 6:57

score 322 · Answer 13 · 2026-04-11 18:09:45

322

Views

How to prove the lower semi-continuity of this functionnal on $H^1(\Omega)$

Published on 11 Apr 2026 - 18:09

score 174 · Answer 14 · 2026-04-17 03:41:03

174

Views

Proof that a particular subset of $L^2[\Pi]$ is dense and first category set (Baire's category)

Published on 17 Apr 2026 - 3:41

score 255 · Answer 15 · 2026-04-17 08:10:33

255

Views

$f_n\xrightarrow{L^p}f \implies f_n'\xrightarrow{L^p}f'$?

Published on 17 Apr 2026 - 8:10

List Question

Is every bounded function in $L^p$ for any $p \ge 1$?

$L^0( \mathbb P | \mathcal F_0 ; || \cdot ||_{\mathbb R^d} ) \subset L^0( \mathbb P | \mathcal F_1 ; || \cdot ||_{\mathbb R^d} ) $?

Seemingly simple inequality between $L_p$ norms (When is $\|f\|_p \leq \|f\|_2$?)

Continuity in the mean: $\lim_{y \to 0}\int_{\mathbb{R}^d}|f(x+y)-f(x)|dx=0$

Examples of $L^p \cap L^1$ convergence

Study the convergence of this sequence in $L^{2}(\mathbb{R})$

How can we show $\left\|g\ast f\right\|_{L^p}\le\left\|g\right\|_{L^1}\left\|f\right\|_{L^p}$?

How to prove this function is $L^{r}(E)$

Q: Exercise 6.R Bartle

Can the limit of a sequence of functions in $L_p$ and the limit in almost everywhere convergence be different?

Weak* convergence in $L^\infty$ and the strong convergence in $L^2$ of a mollification?

Relations between Bochner spaces $L^p(0,T;L^q)$

How to prove the lower semi-continuity of this functionnal on $H^1(\Omega)$

Proof that a particular subset of $L^2[\Pi]$ is dense and first category set (Baire's category)

$f_n\xrightarrow{L^p}f \implies f_n'\xrightarrow{L^p}f'$?

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