Question

Let $M_a$ be a multiplication operator ($M_a u = a(x) u(x)$) and $a \in L_{\infty} (\Omega)$. Show, that $\|M_a\| = \|a\|_{\infty}$.

score 39 · Answer 1 · 2026-04-17 00:05:46

39

Views

Let $M_a$ be a multiplication operator ($M_a u = a(x) u(x)$) and $a \in L_{\infty} (\Omega)$. Show, that $\|M_a\| = \|a\|_{\infty}$.

Published on 17 Apr 2026 - 0:05

score 20 · Answer 2 · 2026-04-15 22:42:15

20

Views

Prove the boundedness of $R(z; D)v(x) = -i \int_x^{\infty} e^{i z(x-y)} v(y) dy, \quad x \in \mathbb{R}_+ \ a.e.$ in $L_1 (\mathbb{R}_+)$

Published on 15 Apr 2026 - 22:42

score 84 · Answer 3 · 2026-04-13 22:43:13

84

Views

Convergence of infinite series of random variables

Published on 13 Apr 2026 - 22:43

score 63 · Answer 4 · 2026-04-17 09:34:14

63

Views

$\lim_{t \to \infty}t^p P[|X|>t]=0$ then $X \in L_{q}$

Published on 17 Apr 2026 - 9:34

score 44 · Answer 5 · 2026-04-14 14:47:38

44

Views

Is this set dense in $L^2$?

Published on 14 Apr 2026 - 14:47

score 225 · Answer 6 · 2026-04-16 08:17:44

225

Views

Every bounded sequence in $\ell_p$ has a weakly convergent subsequence

Published on 16 Apr 2026 - 8:17

score 70 · Answer 7 · 2026-04-15 05:03:14

70

Views

How to denote $L_p$ norm of a matrix $X$ in either row or column direction?

Published on 15 Apr 2026 - 5:03

score 110 · Answer 8 · 2026-04-13 15:13:23

110

Views

$L^p$-space and lebesgue measure

Published on 13 Apr 2026 - 15:13

score 167 · Answer 9 · 2026-05-10 17:38:38

167

Views

Derivation of Hölder Inequality through Young's Inequaliy

Published on 10 May 2026 - 17:38

score 52 · Answer 10 · 2026-04-11 19:13:33

52

Views

Prove that $\lim_{t \to 0^+} \sum_i \frac{|a_i+tv_i| - |a_i|}{t} = \sum_i v_i$

Published on 11 Apr 2026 - 19:13

score 144 · Answer 11 · 2026-04-13 03:36:50

144

Views

Rough estimation for $L^2$ norm of sum of random variables

Published on 13 Apr 2026 - 3:36

score 230 · Answer 12 · 2026-04-12 06:23:42

230

Views

$\sum f_n$ converges in $L^p(\mu)$ implies $\|f_n\|_p \to 0$ as $n\to\infty$.

Published on 12 Apr 2026 - 6:23

score 31 · Answer 13 · 2026-04-16 09:48:48

31

Views

$f\in \mathcal{L}^p$ iff $\sum_{n=1}^{\infty} n^p \mu(A_n)<\infty$

Published on 16 Apr 2026 - 9:48

score 96 · Answer 14 · 2026-04-15 11:44:54

96

Views

L^p inequality for product of random variables

Published on 15 Apr 2026 - 11:44

score 58 · Answer 15 · 2026-04-15 20:55:35

58

Views

Need Proof or Counter-example regarding a certain $L^p$ function

Published on 15 Apr 2026 - 20:55

List Question

Let $M_a$ be a multiplication operator ($M_a u = a(x) u(x)$) and $a \in L_{\infty} (\Omega)$. Show, that $\|M_a\| = \|a\|_{\infty}$.

Prove the boundedness of $R(z; D)v(x) = -i \int_x^{\infty} e^{i z(x-y)} v(y) dy, \quad x \in \mathbb{R}_+ \ a.e.$ in $L_1 (\mathbb{R}_+)$

Convergence of infinite series of random variables

$\lim_{t \to \infty}t^p P[|X|>t]=0$ then $X \in L_{q}$

Is this set dense in $L^2$?

Every bounded sequence in $\ell_p$ has a weakly convergent subsequence

How to denote $L_p$ norm of a matrix $X$ in either row or column direction?

$L^p$-space and lebesgue measure

Derivation of Hölder Inequality through Young's Inequaliy

Prove that $\lim_{t \to 0^+} \sum_i \frac{|a_i+tv_i| - |a_i|}{t} = \sum_i v_i$

Rough estimation for $L^2$ norm of sum of random variables

$\sum f_n$ converges in $L^p(\mu)$ implies $\|f_n\|_p \to 0$ as $n\to\infty$.

$f\in \mathcal{L}^p$ iff $\sum_{n=1}^{\infty} n^p \mu(A_n)<\infty$

L^p inequality for product of random variables

Need Proof or Counter-example regarding a certain $L^p$ function

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