Question

Show that $L^3(\mathbb{R})\setminus L^2(\mathbb{R})$ is non-empty

score 44 · Answer 1 · 2026-04-15 18:33:43

44

Views

Show that $L^3(\mathbb{R})\setminus L^2(\mathbb{R})$ is non-empty

Published on 15 Apr 2026 - 18:33

score 522 · Answer 2 · 2026-04-12 12:20:41

522

Views

Understanding $L^1 \cap L^\infty$

Published on 12 Apr 2026 - 12:20

score 564 · Answer 3 · 2026-04-13 04:40:18

564

Views

Showing step functions with rational endpoints are $L^p$-dense

Published on 13 Apr 2026 - 4:40

score 37 · Answer 4 · 2026-04-15 14:34:16

37

Views

What is the difference between $ \| g\|_{q}^{q}$ and $ \| g\|_{q}$?

Published on 15 Apr 2026 - 14:34

score 31 · Answer 5 · 2026-04-10 23:59:07

31

Views

If a series is convergent is it possible to perform mathematical operations with its sum?

Published on 10 Apr 2026 - 23:59

score 178 · Answer 6 · 2026-04-15 11:23:34

178

Views

Sobolev Inequality for $u \in W_{0}^{1,p}(\mathbb{R}^{n})$.

Published on 15 Apr 2026 - 11:23

score 103 · Answer 7 · 2026-04-16 22:17:09

103

Views

If a sequence $(u_n)$ in $L^p \cap L^q$ converges to $u$ in $L^p$ and to $v$ in $L^q$, then $u=v$ a.e.

Published on 16 Apr 2026 - 22:17

score 216 · Answer 8 · 2026-04-11 07:09:55

216

Views

Properties of Lebesgue Spaces

Published on 11 Apr 2026 - 7:09

score 51 · Answer 9 · 2026-04-16 03:11:08

51

Views

must any $\phi \in \operatorname{Hom}_G(V, L^2(G))$ be continuous?

Published on 16 Apr 2026 - 3:11

score 195 · Answer 10 · 2026-04-16 03:35:35

195

Views

The dual of $\ell^p(\textbf{r})$ is $\ell^q(\textbf{r})$, where $\textbf{r}$ is a weighted vector

Published on 16 Apr 2026 - 3:35

score 136 · Answer 11 · 2026-04-16 19:49:04

136

Views

Must any $\phi \in \operatorname{Hom}_G(V, L^2(G))$ have continuous values?

Published on 16 Apr 2026 - 19:49

score 357 · Answer 12 · 2026-04-16 14:01:43

357

Views

If $f$ is Lebesgue integrable and $f''$ exists and is Lebesgue integrable, what can we say about the integrability of $f'$?

Published on 16 Apr 2026 - 14:01

score 46 · Answer 13 · 2026-04-15 07:59:25

46

Views

Group algebra and $L^\infty$ of Pontryagin dual group correspondence

Published on 15 Apr 2026 - 7:59

score 671 · Answer 14 · 2026-04-14 12:41:01

671

Views

Describe all the compact subsets of $\ell^{1}$ -- General Result Proved, Example Needed.

Published on 14 Apr 2026 - 12:41

score 221 · Answer 15 · 2026-04-14 19:08:11

221

Views

Expectation and $L^p$ space (subgaussian random variable)

Published on 14 Apr 2026 - 19:08

List Question

Show that $L^3(\mathbb{R})\setminus L^2(\mathbb{R})$ is non-empty

Understanding $L^1 \cap L^\infty$

Showing step functions with rational endpoints are $L^p$-dense

What is the difference between $ \| g\|_{q}^{q}$ and $ \| g\|_{q}$?

If a series is convergent is it possible to perform mathematical operations with its sum?

Sobolev Inequality for $u \in W_{0}^{1,p}(\mathbb{R}^{n})$.

If a sequence $(u_n)$ in $L^p \cap L^q$ converges to $u$ in $L^p$ and to $v$ in $L^q$, then $u=v$ a.e.

Properties of Lebesgue Spaces

must any $\phi \in \operatorname{Hom}_G(V, L^2(G))$ be continuous?

The dual of $\ell^p(\textbf{r})$ is $\ell^q(\textbf{r})$, where $\textbf{r}$ is a weighted vector

Must any $\phi \in \operatorname{Hom}_G(V, L^2(G))$ have continuous values?

If $f$ is Lebesgue integrable and $f''$ exists and is Lebesgue integrable, what can we say about the integrability of $f'$?

Group algebra and $L^\infty$ of Pontryagin dual group correspondence

Describe all the compact subsets of $\ell^{1}$ -- General Result Proved, Example Needed.

Expectation and $L^p$ space (subgaussian random variable)

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