Question

Proof of separability of $L^p$ spaces

score 20.1k · Answer 1 · 2014-07-26 19:08:18

20.1k

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Proof of separability of $L^p$ spaces

Published on 26 Jul 2014 - 19:08

score 288 · Answer 2 · 2014-07-26 21:17:02

288

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Convergence in $L^p$ by using Holder's inequality

Published on 26 Jul 2014 - 21:17

score 154 · Answer 3 · 2014-07-26 23:19:36

154

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Is a linear operator on $\ell^2$ defined by the inner product necessarily bounded?

Published on 26 Jul 2014 - 23:19

score 4.3k · Answer 4 · 2026-03-25 22:10:39

4.3k

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Uniform integrability of a function in $L^1$

Published on 25 Mar 2026 - 22:10

score 352 · Answer 5 · 2014-07-29 13:36:28

352

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Given $f_n \rightarrow f$ a.e. Does $||f_n||_p \rightarrow ||f||_p$ imply $f_n\rightarrow f$ in $L^p$?

Published on 29 Jul 2014 - 13:36

score 338 · Answer 6 · 2026-03-30 08:32:39

338

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Questions about $L^p$ spaces and convergences

Published on 30 Mar 2026 - 8:32

score 454 · Answer 7 · 2026-03-26 11:05:01

454

Views

Canonical inclusion $L^q(0,1) \to L^p(0,1)$ is compact?

Published on 26 Mar 2026 - 11:05

score 76 · Answer 8 · 2014-07-31 21:54:33

76

Views

Use the uncertainty principle to prove that $\int_{\mathbb R^n} (f(x))^2|\hat{f}(x)|^2 \,dx=0$ if and only if $f\equiv 0$.

Published on 31 Jul 2014 - 21:54

score 232 · Answer 9 · 2026-03-30 08:36:44

232

Views

Weak convergence $f_n \rightharpoonup f$ in $L^2(\mathbb{R})$ and $f_n^2 \rightharpoonup g$ in $L^1(\mathbb{R})$ implies $f^2\leq g$ a.e.

Published on 30 Mar 2026 - 8:36

score 191 · Answer 10 · 2026-03-25 21:48:00

191

Views

Why does duality imply, that it is enough to consider p>2.

Published on 25 Mar 2026 - 21:48

score 652 · Answer 11 · 2014-08-02 11:01:41

652

Views

Domain of multiplication operator

Published on 02 Aug 2014 - 11:01

score 1.6k · Answer 12 · 2026-04-02 11:43:43

1.6k

Views

Properties of a set in $\ell^2$ space

Published on 02 Apr 2026 - 11:43

score 261 · Answer 13 · 2026-04-01 00:28:28

261

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Is Sobolev space $H^{s}(\mathbb R),$ for $s>\frac{1}{2},$ closed under point wise multiplication?

Published on 01 Apr 2026 - 0:28

score 64 · Answer 14 · 2026-04-01 00:26:37

64

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Can we expect, $h\ast \mu \in L^{2}(\mathbb R, (1+|x|^{2})^{s})$ for $h\in \mathcal{S}(\mathbb R), \mu\in M(\mathbb R)$ and $s>1/2$?

Published on 01 Apr 2026 - 0:26

score 1.1k · Answer 15 · 2026-03-30 22:14:22

1.1k

Views

The existence of conditional expectation with respect to a sub-$\sigma$-algebra

Published on 30 Mar 2026 - 22:14

List Question

Proof of separability of $L^p$ spaces

Convergence in $L^p$ by using Holder's inequality

Is a linear operator on $\ell^2$ defined by the inner product necessarily bounded?

Uniform integrability of a function in $L^1$

Given $f_n \rightarrow f$ a.e. Does $||f_n||_p \rightarrow ||f||_p$ imply $f_n\rightarrow f$ in $L^p$?

Questions about $L^p$ spaces and convergences

Canonical inclusion $L^q(0,1) \to L^p(0,1)$ is compact?

Use the uncertainty principle to prove that $\int_{\mathbb R^n} (f(x))^2|\hat{f}(x)|^2 \,dx=0$ if and only if $f\equiv 0$.

Weak convergence $f_n \rightharpoonup f$ in $L^2(\mathbb{R})$ and $f_n^2 \rightharpoonup g$ in $L^1(\mathbb{R})$ implies $f^2\leq g$ a.e.

Why does duality imply, that it is enough to consider p>2.

Domain of multiplication operator

Properties of a set in $\ell^2$ space

Is Sobolev space $H^{s}(\mathbb R),$ for $s>\frac{1}{2},$ closed under point wise multiplication?

Can we expect, $h\ast \mu \in L^{2}(\mathbb R, (1+|x|^{2})^{s})$ for $h\in \mathcal{S}(\mathbb R), \mu\in M(\mathbb R)$ and $s>1/2$?

The existence of conditional expectation with respect to a sub-$\sigma$-algebra

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