Question

Proof of $\big|\int_E (f\cdot g)(x) \text{d}x\big| \leq [\int_E |f(x)|^p\text{d}x]^{(1/p)} \cdot [\int_E |g(x)| ^q\text{d}x]^{(1/q)}$

score 98 · Answer 1 · 2026-03-22 19:20:42

98

Views

Proof of $\big|\int_E (f\cdot g)(x) \text{d}x\big| \leq [\int_E |f(x)|^p\text{d}x]^{(1/p)} \cdot [\int_E |g(x)| ^q\text{d}x]^{(1/q)}$

Published on 22 Mar 2026 - 19:20

score 88 · Answer 2 · 2018-02-03 17:26:56

88

Views

Is the map $T: C(X) \to \mathbb{B}(L^2(X,\nu))$ defined by $T(f)=M_f$, where $M_f(g)=fg$, injective?

Published on 03 Feb 2018 - 17:26

score 22 · Answer 3 · 2018-02-03 17:44:35

22

Views

Is it true that $\|u^{a}\|_{L^\infty }=\|u\|_{L^\infty }^a$ where $a>0$?

Published on 03 Feb 2018 - 17:44

score 87 · Answer 4 · 2018-02-03 23:56:07

87

Views

If $f\in L^{1}((0,1))$, does it hold that $\lim\limits_{n\to+\infty}\int_{0}^{\frac{1}{n}}f(x)\mathrm{d}x=0$?

Published on 03 Feb 2018 - 23:56

score 51 · Answer 5 · 2018-02-04 23:46:32

51

Views

Is the set of continuous function that are also $\mathcal{L}^1(\mathbb{R})$ a subset of $\mathcal{L}^2(\mathbb{R})$

Published on 04 Feb 2018 - 23:46

score 68 · Answer 6 · 2018-02-05 22:06:40

68

Views

A finite-codimensional subspace of the space of [square-integrable] holomorphic functions

Published on 05 Feb 2018 - 22:06

score 1k · Answer 7 · 2026-03-17 10:11:54

1k

Views

Failing to prove that E(XY) is an inner product

Published on 17 Mar 2026 - 10:11

score 35 · Answer 8 · 2018-02-07 22:35:20

35

Views

Condition on $\nu$ which makes the inclusion map from $C(X)$ to $L^{\infty}(X)$ injective

Published on 07 Feb 2018 - 22:35

score 26 · Answer 9 · 2026-03-22 10:30:19

26

Views

When does an action on $X$ makes an well defined action on $L^{\infty}(X)$?

Published on 22 Mar 2026 - 10:30

score 2k · Answer 10 · 2018-02-08 21:28:46

2k

Views

How are $L^P$ spaces defined for complex valued functions?

Published on 08 Feb 2018 - 21:28

score 455 · Answer 11 · 2026-03-22 19:30:30

455

Views

Equivalence between squared-norm and norm inequalities

Published on 22 Mar 2026 - 19:30

score 270 · Answer 12 · 2026-03-22 05:16:29

270

Views

Norms of higher order Lp spaces

Published on 22 Mar 2026 - 5:16

score 85 · Answer 13 · 2018-02-09 23:31:12

85

Views

Why is it nonsensical to evaluate $f(0)$ for $f\in L^p$?

Published on 09 Feb 2018 - 23:31

score 430 · Answer 14 · 2026-03-22 02:08:11

430

Views

Duality between $L^\infty$ and $L^1$

Published on 22 Mar 2026 - 2:08

score 105 · Answer 15 · 2026-03-22 12:19:13

105

Views

Convergence in norm equivalent formulations

Published on 22 Mar 2026 - 12:19

List Question

Proof of $\big|\int_E (f\cdot g)(x) \text{d}x\big| \leq [\int_E |f(x)|^p\text{d}x]^{(1/p)} \cdot [\int_E |g(x)| ^q\text{d}x]^{(1/q)}$

Is the map $T: C(X) \to \mathbb{B}(L^2(X,\nu))$ defined by $T(f)=M_f$, where $M_f(g)=fg$, injective?

Is it true that $\|u^{a}\|_{L^\infty }=\|u\|_{L^\infty }^a$ where $a>0$?

If $f\in L^{1}((0,1))$, does it hold that $\lim\limits_{n\to+\infty}\int_{0}^{\frac{1}{n}}f(x)\mathrm{d}x=0$?

Is the set of continuous function that are also $\mathcal{L}^1(\mathbb{R})$ a subset of $\mathcal{L}^2(\mathbb{R})$

A finite-codimensional subspace of the space of [square-integrable] holomorphic functions

Failing to prove that E(XY) is an inner product

Condition on $\nu$ which makes the inclusion map from $C(X)$ to $L^{\infty}(X)$ injective

When does an action on $X$ makes an well defined action on $L^{\infty}(X)$?

How are $L^P$ spaces defined for complex valued functions?

Equivalence between squared-norm and norm inequalities

Norms of higher order Lp spaces

Why is it nonsensical to evaluate $f(0)$ for $f\in L^p$?

Duality between $L^\infty$ and $L^1$

Convergence in norm equivalent formulations

Trending Questions

Popular # Hahtags

Popular Questions