List questions from lp-spaces

Published on 14 Apr 2026 - 23:11

267

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Showing that $1/\sqrt{x}\in L^1$ by finding Cauchy sequence that converges to it

Published on 13 Apr 2026 - 3:46

28

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Does the pointwise limit of a $W^{r,p}$- bounded sequence belong to $W^{r,p}$?

Published on 14 May 2026 - 5:00

90

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Does Hölder's Inequality implies that $\int_{-\infty}^\infty |f(t) \,g(t)|\,\mathrm dt \leq \int_{-\infty}^\infty |f(t)|\,\mathrm dt \, \sup |g|$?

Published on 16 Apr 2026 - 8:06

153

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There exists any real functions $f(t)$ on $[-1; 1]$ with $f(-1)\neq 0$ such $\lim_{w \to \infty} |w\cdot \int_{-1}^1 e^{-iwt}f(t)\,dt| = 0$?

Published on 16 Apr 2026 - 3:39

195

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Counter example to $L^{p}$ , $L^{q}$ inclusion on infinite measure spaces

Published on 15 Apr 2026 - 15:09

374

Views

Law of large numbers with convergence in mean

Published on 12 Apr 2026 - 6:10

132

Views

Hanner inequality: reduction to non-negative functions

Published on 13 Apr 2026 - 1:31

44

Views

In $l^p$ the map $x\longrightarrow \sum_{n=1}^\infty x_ny_n$ is well-defined.

Published on 16 Apr 2026 - 10:48

42

Views

How to recover the classical real number $\mathbb E[Y |X=x]$ from the $L_2$-definition of $\mathbb E[Y |X=x]$?

Published on 24 Apr 2026 - 20:59

37

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$W_0^{1,1}([0,+\infty)) \subset L^\infty((0,\infty))$?

Published on 14 May 2026 - 5:00

51

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Integral of an $L^p(\mathbb R^2)$ function is in $L^p(\mathbb R)$?

Published on 14 Apr 2026 - 12:06

38

Views

Sequence in $C_c(X)$ converging to $f$ in all possible $\mathscr{L}^p$

Published on 16 Apr 2026 - 7:59

95

Views

Compact set in $L^1(0,1)$

Published on 13 Apr 2026 - 6:41

76

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Clarifying $L^p$ convergence

Published on 17 Apr 2026 - 7:35

List Question

Brezis exercise 3.20

Showing that $1/\sqrt{x}\in L^1$ by finding Cauchy sequence that converges to it

Does the pointwise limit of a $W^{r,p}$- bounded sequence belong to $W^{r,p}$?

Does Hölder's Inequality implies that $\int_{-\infty}^\infty |f(t) \,g(t)|\,\mathrm dt \leq \int_{-\infty}^\infty |f(t)|\,\mathrm dt \, \sup |g|$?

There exists any real functions $f(t)$ on $[-1; 1]$ with $f(-1)\neq 0$ such $\lim_{w \to \infty} |w\cdot \int_{-1}^1 e^{-iwt}f(t)\,dt| = 0$?

Counter example to $L^{p}$ , $L^{q}$ inclusion on infinite measure spaces

Law of large numbers with convergence in mean

Hanner inequality: reduction to non-negative functions

In $l^p$ the map $x\longrightarrow \sum_{n=1}^\infty x_ny_n$ is well-defined.

How to recover the classical real number $\mathbb E[Y |X=x]$ from the $L_2$-definition of $\mathbb E[Y |X=x]$?

$W_0^{1,1}([0,+\infty)) \subset L^\infty((0,\infty))$?

Integral of an $L^p(\mathbb R^2)$ function is in $L^p(\mathbb R)$?

Sequence in $C_c(X)$ converging to $f$ in all possible $\mathscr{L}^p$

Compact set in $L^1(0,1)$

Clarifying $L^p$ convergence

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