Question

For what values of $ p \in (0, \infty] $ do we have $ f \in L^p (\mathbb{R}^3) $?

score 66 · Answer 1 · 2019-10-29 01:24:51

66

Views

For what values of $ p \in (0, \infty] $ do we have $ f \in L^p (\mathbb{R}^3) $?

Published on 29 Oct 2019 - 1:24

score 38 · Answer 2 · 2019-10-29 16:26:48

38

Views

Let $u(x)=(x^{\alpha}+x^{\beta})^{-1}$ $x,\alpha,\beta>0$. Find $p\geq 1$, $u\in\mathcal L^p(\lambda^1,(0,\infty))$

Published on 29 Oct 2019 - 16:26

score 58 · Answer 3 · 2019-10-30 17:24:48

58

Views

Does convergence in $L^2$ imply convergence on $\mathbb R$?

Published on 30 Oct 2019 - 17:24

score 319 · Answer 4 · 2019-10-31 04:29:10

319

Views

Proving $\int f_n gd \mu \to \int f g d\mu$ for $f \in L^p, g \in L^q$ where $p$ and $q$ are Holder conjugate exponents.

Published on 31 Oct 2019 - 4:29

score 68 · Answer 5 · 2026-04-03 07:12:13

68

Views

$\sum_{k=1}^{\infty}|a_kb_k| < \infty$ $\forall \sum_{k=1}^\infty|a_k|$ convergent. Prove $\{b_k\}_{k=1}^\infty$ is bounded. For continuous functions?

Published on 03 Apr 2026 - 7:12

score 81 · Answer 6 · 2019-11-01 18:07:34

81

Views

Proving inclusion $L^q \subseteq L^p$ for $1 \leq p \leq q \leq \infty$

Published on 01 Nov 2019 - 18:07

score 219 · Answer 7 · 2026-04-02 02:01:30

219

Views

Show that $\bigcap_{p<\infty }\mathcal{L}^p([0,1])\neq \mathcal{L}^{\infty }([0,1])$

Published on 02 Apr 2026 - 2:01

score 41 · Answer 8 · 2019-11-02 04:49:26

Showing or refuting $L^1(\mathbb{R}^n)\cap L^p(\mathbb{R}^n)$ is dense in $L^p(\mathbb{R}^n)$ for $1\leq p\leq \infty$?

score 79 · Answer 9 · 2026-03-26 17:36:05

79

Views

Weird mistake that I cannot spot in a proof

Published on 26 Mar 2026 - 17:36

score 71 · Answer 10 · 2026-02-23 12:31:32

71

Views

Weak, Strong, a.e. convergence parameters in $L^2(R^3)$ excercise

Published on 23 Feb 2026 - 12:31

score 440 · Answer 11 · 2026-04-03 08:50:49

440

Views

If $fh\in \mathcal{L}^1(\mu )$ for every $h\in \mathcal{L}^{p'}(\mu )$ then $f\in \mathcal{L}^p(\mu)$

Published on 03 Apr 2026 - 8:50

score 363 · Answer 12 · 2019-11-04 18:13:45

363

Views

Fourier Exercise (Folland 8.18)

Published on 04 Nov 2019 - 18:13

score 189 · Answer 13 · 2026-04-02 01:55:34

189

Views

is $H^{1}\left(\Omega\right)\cap L^{\infty}\left(\Omega\right)$ closed in $H^{1}\left(\Omega\right)$?

Published on 02 Apr 2026 - 1:55

score 103 · Answer 14 · 2026-04-01 14:22:38

103

Views

Modulus of continuity and Hölder's inequality

Published on 01 Apr 2026 - 14:22

score 163 · Answer 15 · 2019-11-05 07:17:53

163

Views

Some kind of inverted Minkowski's inequality?

Published on 05 Nov 2019 - 7:17

List Question

For what values of $ p \in (0, \infty] $ do we have $ f \in L^p (\mathbb{R}^3) $?

Let $u(x)=(x^{\alpha}+x^{\beta})^{-1}$ $x,\alpha,\beta>0$. Find $p\geq 1$, $u\in\mathcal L^p(\lambda^1,(0,\infty))$

Does convergence in $L^2$ imply convergence on $\mathbb R$?

Proving $\int f_n gd \mu \to \int f g d\mu$ for $f \in L^p, g \in L^q$ where $p$ and $q$ are Holder conjugate exponents.

$\sum_{k=1}^{\infty}|a_kb_k| < \infty$ $\forall \sum_{k=1}^\infty|a_k|$ convergent. Prove $\{b_k\}_{k=1}^\infty$ is bounded. For continuous functions?

Proving inclusion $L^q \subseteq L^p$ for $1 \leq p \leq q \leq \infty$

Show that $\bigcap_{p<\infty }\mathcal{L}^p([0,1])\neq \mathcal{L}^{\infty }([0,1])$

Showing or refuting $L^1(\mathbb{R}^n)\cap L^p(\mathbb{R}^n)$ is dense in $L^p(\mathbb{R}^n)$ for $1\leq p\leq \infty$?

Weird mistake that I cannot spot in a proof

Weak, Strong, a.e. convergence parameters in $L^2(R^3)$ excercise

If $fh\in \mathcal{L}^1(\mu )$ for every $h\in \mathcal{L}^{p'}(\mu )$ then $f\in \mathcal{L}^p(\mu)$

Fourier Exercise (Folland 8.18)

is $H^{1}\left(\Omega\right)\cap L^{\infty}\left(\Omega\right)$ closed in $H^{1}\left(\Omega\right)$?

Modulus of continuity and Hölder's inequality

Some kind of inverted Minkowski's inequality?

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