Question

What does the boundary of the set of points closer to the origin than some other fixed point in $\mathbb{R}^d, \|\cdot\|_p$ look like, when $p\neq 2$?

score 76 · Answer 1 · 2026-04-15 03:03:09

76

Views

What does the boundary of the set of points closer to the origin than some other fixed point in $\mathbb{R}^d, \|\cdot\|_p$ look like, when $p\neq 2$?

Published on 15 Apr 2026 - 3:03

score 236 · Answer 2 · 2026-05-06 06:09:22

236

Views

Is there $f \in L^p(\Omega)$ such that given $\epsilon>0$, $f \not \in L^{p+\epsilon}(\Omega)$?

Published on 06 May 2026 - 6:09

score 65 · Answer 3 · 2026-04-29 14:18:59

65

Views

If $f$, $g$ and $fg$ are all in $L^{2}(\mathbb{R}^{n})$, does it follow that $\mathcal{F}(fg)=\mathcal{F}(f)\mathcal{F}(g)$?

Published on 29 Apr 2026 - 14:18

score 103 · Answer 4 · 2026-04-17 01:26:41

103

Views

Proving this sequence of $L^2(\Omega)$ converges

Published on 17 Apr 2026 - 1:26

score 185 · Answer 5 · 2026-04-14 22:55:31

185

Views

Convolution of an $L^2$ function with an $L^1$ function converges

Published on 14 Apr 2026 - 22:55

score 210 · Answer 6 · 2026-04-15 18:44:13

210

Views

$f \in L^p \iff$ a certain series converges

Published on 15 Apr 2026 - 18:44

score 89 · Answer 7 · 2026-05-14 06:18:19

89

Views

Continuity and $L^p$ norm

Published on 14 May 2026 - 6:18

score 75 · Answer 8 · 2026-04-13 21:16:24

75

Views

Equality in ${L^{2}}{(0,1)}$

Published on 13 Apr 2026 - 21:16

score 33 · Answer 9 · 2026-04-16 16:41:27

33

Views

How can we show $\left\|f-g\right\|_{L^p(\mu)}^p\le2^{p-2}\left\|f-g\right\|_{L^2(\mu)}^2$? if $p>2$ and $|f|,|g|\le1$?

Published on 16 Apr 2026 - 16:41

score 234 · Answer 10 · 2026-04-16 08:50:13

234

Views

$L^1_{loc}(\mathbb{R})$ is a Fréchet space

Published on 16 Apr 2026 - 8:50

score 25 · Answer 11 · 2026-04-16 07:57:19

25

Views

Denseness of $\ell_1$ in a bigger normed vector space of sequences

Published on 16 Apr 2026 - 7:57

score 487 · Answer 12 · 2026-04-14 05:43:46

487

Views

When is $L^1$ a dual space?

Published on 14 Apr 2026 - 5:43

score 131 · Answer 13 · 2026-04-15 05:05:24

131

Views

Why $L^2(\Omega) \hookrightarrow H^{-1}$?

Published on 15 Apr 2026 - 5:05

score 76 · Answer 14 · 2026-04-13 05:33:01

76

Views

Convergence of integrals in $L^p$(convergence in $L^1$)

Published on 13 Apr 2026 - 5:33

score 49 · Answer 15 · 2026-04-16 01:50:02

49

Views

Measures and $\mathcal{L}_\infty$ space

Published on 16 Apr 2026 - 1:50

List Question

What does the boundary of the set of points closer to the origin than some other fixed point in $\mathbb{R}^d, \|\cdot\|_p$ look like, when $p\neq 2$?

Is there $f \in L^p(\Omega)$ such that given $\epsilon>0$, $f \not \in L^{p+\epsilon}(\Omega)$?

If $f$, $g$ and $fg$ are all in $L^{2}(\mathbb{R}^{n})$, does it follow that $\mathcal{F}(fg)=\mathcal{F}(f)\mathcal{F}(g)$?

Proving this sequence of $L^2(\Omega)$ converges

Convolution of an $L^2$ function with an $L^1$ function converges

$f \in L^p \iff$ a certain series converges

Continuity and $L^p$ norm

Equality in ${L^{2}}{(0,1)}$

How can we show $\left\|f-g\right\|_{L^p(\mu)}^p\le2^{p-2}\left\|f-g\right\|_{L^2(\mu)}^2$? if $p>2$ and $|f|,|g|\le1$?

$L^1_{loc}(\mathbb{R})$ is a Fréchet space

Denseness of $\ell_1$ in a bigger normed vector space of sequences

When is $L^1$ a dual space?

Why $L^2(\Omega) \hookrightarrow H^{-1}$?

Convergence of integrals in $L^p$(convergence in $L^1$)

Measures and $\mathcal{L}_\infty$ space

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