Question

For what $p,q\in [1,\infty]$ and given $f\in L_p$, $g\in L_q$ is $f\cdot g^2\in L_1$?

score 68 · Answer 1 · 2026-04-17 03:00:59

68

Views

For what $p,q\in [1,\infty]$ and given $f\in L_p$, $g\in L_q$ is $f\cdot g^2\in L_1$?

Published on 17 Apr 2026 - 3:00

score 230 · Answer 2 · 2026-04-13 22:04:21

230

Views

Showing $c_{00}$ dense in $\ell^p$

Published on 13 Apr 2026 - 22:04

score 65 · Answer 3 · 2026-04-16 10:55:30

65

Views

Intuitive implication of the fact that dual of $L_{p}$-norm space is $L_{q}$-norm space where $\frac{1}{p}+\frac{1}{q}=1$.

Published on 16 Apr 2026 - 10:55

score 66 · Answer 4 · 2026-04-16 03:49:10

66

Views

For what parameter $a\in[0,\infty)$ is $\|\frac{|x|^2}{1+|x|^a}\|_{L_2}<\infty$?

Published on 16 Apr 2026 - 3:49

score 35 · Answer 5 · 2026-04-14 14:19:46

35

Views

How to understand this equation $L(L^2(a,b), \mathbb{R}) = L^2(a,b)$?

Published on 14 Apr 2026 - 14:19

score 79 · Answer 6 · 2026-04-12 08:32:28

79

Views

A question about inclusion of $\mathcal L^p$ spaces for a general measure space

Published on 12 Apr 2026 - 8:32

score 96 · Answer 7 · 2026-04-16 09:31:59

96

Views

Show that an $L^p$-convergent martingale is almost surely convergent

Published on 16 Apr 2026 - 9:31

score 41 · Answer 8 · 2026-04-15 22:24:16

41

Views

If $f_n \rightarrow f$ in $L^\infty$ then $\| f_h \|_\infty \rightarrow \| f \|_\infty$

Published on 15 Apr 2026 - 22:24

score 292 · Answer 9 · 2026-05-05 22:33:41

292

Views

Embedding $BV$ into $L^p$

Published on 05 May 2026 - 22:33

score 161 · Answer 10 · 2026-05-05 17:38:26

161

Views

Counterexample for $L^p$-convergence

Published on 05 May 2026 - 17:38

score 106 · Answer 11 · 2026-04-14 14:48:17

106

Views

Query in the proof of $\overline{C_c(X)}=L^p(\mu)$ of Rudin's Real & Complex Analysis (Theorem 3.14)

Published on 14 Apr 2026 - 14:48

score 37 · Answer 12 · 2026-04-12 18:47:17

37

Views

Asymptotic of Unitary operator and orthogonal complement

Published on 12 Apr 2026 - 18:47

score 57 · Answer 13 · 2026-04-16 13:56:57

57

Views

If $1 \le p \le q \le \infty $, then $L^q (\Omega) \subset L^p_{loc} (\Omega) $.

Published on 16 Apr 2026 - 13:56

score 253 · Answer 14 · 2026-04-15 17:28:37

253

Views

Corollary Hölder's inequality: $\Vert f \Vert_p=\sup_{\{g\::\:\Vert g\Vert _q=1\}}\int fg$

Published on 15 Apr 2026 - 17:28

score 119 · Answer 15 · 2026-04-15 20:56:12

119

Views

Non-existence of surjections from $L^p$ to $L^q$

Published on 15 Apr 2026 - 20:56

List Question

For what $p,q\in [1,\infty]$ and given $f\in L_p$, $g\in L_q$ is $f\cdot g^2\in L_1$?

Showing $c_{00}$ dense in $\ell^p$

Intuitive implication of the fact that dual of $L_{p}$-norm space is $L_{q}$-norm space where $\frac{1}{p}+\frac{1}{q}=1$.

For what parameter $a\in[0,\infty)$ is $\|\frac{|x|^2}{1+|x|^a}\|_{L_2}<\infty$?

How to understand this equation $L(L^2(a,b), \mathbb{R}) = L^2(a,b)$?

A question about inclusion of $\mathcal L^p$ spaces for a general measure space

Show that an $L^p$-convergent martingale is almost surely convergent

If $f_n \rightarrow f$ in $L^\infty$ then $\| f_h \|_\infty \rightarrow \| f \|_\infty$

Embedding $BV$ into $L^p$

Counterexample for $L^p$-convergence

Query in the proof of $\overline{C_c(X)}=L^p(\mu)$ of Rudin's Real & Complex Analysis (Theorem 3.14)

Asymptotic of Unitary operator and orthogonal complement

If $1 \le p \le q \le \infty $, then $L^q (\Omega) \subset L^p_{loc} (\Omega) $.

Corollary Hölder's inequality: $\Vert f \Vert_p=\sup_{\{g\::\:\Vert g\Vert _q=1\}}\int fg$

Non-existence of surjections from $L^p$ to $L^q$

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