Question

Implication of Sobolev inequality

score 64 · Answer 1 · 2026-05-06 01:20:44

64

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Implication of Sobolev inequality

Published on 06 May 2026 - 1:20

score 104 · Answer 2 · 2026-04-15 08:05:43

104

Views

Necessary and sufficient condition for $l_p$ space inclusion

Published on 15 Apr 2026 - 8:05

score 66 · Answer 3 · 2026-04-15 01:20:21

66

Views

$X_n\stackrel{P}{\to} c$ implies $\mathbb{E}f(X_n){\to} f(c)$ for continuous (but possibly unbounded) $f$

Published on 15 Apr 2026 - 1:20

score 99 · Answer 4 · 2026-04-14 16:48:47

99

Views

How to show $\lim_{n \to \infty}f(x_n)=f(x)?$

Published on 14 Apr 2026 - 16:48

score 48 · Answer 5 · 2026-04-13 02:41:31

48

Views

Let $u:\Omega\subset \mathbb{R}^n\rightarrow \mathbb{R}$ a measureble function. Prove that $u\in L^p(\Omega)$

Published on 13 Apr 2026 - 2:41

score 37 · Answer 6 · 2026-04-17 11:02:27

37

Views

Let $(a,b)$ and $f\in L_{\text{loc}}^1(a,b)$. For $x_0\in (a,b)$, $F(t)=\int_{x_0}^{t}f(s)ds$. Prove that, $DF=f$ (towards theoretical distribution).

Published on 17 Apr 2026 - 11:02

score 1.4k · Answer 7 · 2026-04-12 02:29:02

1.4k

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Definition of weak* convergence in $L^{\infty}$

Published on 12 Apr 2026 - 2:29

score 254 · Answer 8 · 2026-04-13 18:46:27

254

Views

Showing relatively compact and finite dimension

Published on 13 Apr 2026 - 18:46

score 444 · Answer 9 · 2026-03-23 08:25:10

444

Views

About the proof of Minkowski generalized integral inequality

Published on 23 Mar 2026 - 8:25

score 138 · Answer 10 · 2026-05-06 02:20:08

138

Views

A problem on weak convergence: weak convergence of a sequence implies the weak convergence of the square of this sequence?

Published on 06 May 2026 - 2:20

score 67 · Answer 11 · 2026-04-17 14:08:02

67

Views

If $f\in L^2[0,1]$ such that $\int_0^x f(t)\ dt=0$ for all $x\in [0,1]$. Prove that $f=0$ in $L^2[0,1]$

Published on 17 Apr 2026 - 14:08

score 304 · Answer 12 · 2026-04-15 17:50:38

304

Views

Orthogonal decomposition of the periodic space $L^2$

Published on 15 Apr 2026 - 17:50

score 39 · Answer 13 · 2026-04-14 23:23:40

39

Views

comparison of norms two sequences in $\ell_1$ space

Published on 14 Apr 2026 - 23:23

score 65 · Answer 14 · 2026-04-16 15:10:56

65

Views

Is $\mathcal{B}(L^p,L^1)$ strictly bigger than $L^q$?

Published on 16 Apr 2026 - 15:10

score 150 · Answer 15 · 2026-05-06 02:21:08

150

Views

The inclusion of $W^{1,p}$, $p\geq1$ into $C[0,1]$ with sup norm is bounded.

Published on 06 May 2026 - 2:21

List Question

Implication of Sobolev inequality

Necessary and sufficient condition for $l_p$ space inclusion

$X_n\stackrel{P}{\to} c$ implies $\mathbb{E}f(X_n){\to} f(c)$ for continuous (but possibly unbounded) $f$

How to show $\lim_{n \to \infty}f(x_n)=f(x)?$

Let $u:\Omega\subset \mathbb{R}^n\rightarrow \mathbb{R}$ a measureble function. Prove that $u\in L^p(\Omega)$

Let $(a,b)$ and $f\in L_{\text{loc}}^1(a,b)$. For $x_0\in (a,b)$, $F(t)=\int_{x_0}^{t}f(s)ds$. Prove that, $DF=f$ (towards theoretical distribution).

Definition of weak* convergence in $L^{\infty}$

Showing relatively compact and finite dimension

About the proof of Minkowski generalized integral inequality

A problem on weak convergence: weak convergence of a sequence implies the weak convergence of the square of this sequence?

If $f\in L^2[0,1]$ such that $\int_0^x f(t)\ dt=0$ for all $x\in [0,1]$. Prove that $f=0$ in $L^2[0,1]$

Orthogonal decomposition of the periodic space $L^2$

comparison of norms two sequences in $\ell_1$ space

Is $\mathcal{B}(L^p,L^1)$ strictly bigger than $L^q$?

The inclusion of $W^{1,p}$, $p\geq1$ into $C[0,1]$ with sup norm is bounded.

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