Question

Example of a bounded linear functional on $L^p$ space that is not trivially the dual of an $L^q$ function

score 163 · Answer 1 · 2026-04-13 23:06:35

163

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Example of a bounded linear functional on $L^p$ space that is not trivially the dual of an $L^q$ function

Published on 13 Apr 2026 - 23:06

score 428 · Answer 2 · 2026-04-14 11:59:49

428

Views

Prove that a convolution product $(f\ast g)(x)$, with $f,g\in\mathcal{L}^2(\mathbb{R})$, goes to $0$ as $|x|$ goes to $\infty$.

Published on 14 Apr 2026 - 11:59

score 253 · Answer 3 · 2026-04-10 00:55:35

253

Views

Folland Question 6.4 trouble with estimating norm

Published on 10 Apr 2026 - 0:55

score 104 · Answer 4 · 2026-04-10 18:50:13

104

Views

Convergence of $h^{1-p}(f(x+h)-f(x))^{p}$ when $f$ is absolutely continuous and $f' \in L^{p}$

Published on 10 Apr 2026 - 18:50

score 325 · Answer 5 · 2026-04-13 16:09:56

325

Views

l2 compact operator

Published on 13 Apr 2026 - 16:09

score 55 · Answer 6 · 2026-04-15 07:31:46

55

Views

If $u(x):=\int_{x_0}^x v(t)\;dt$, then $u$ locally absolutely continuous.

Published on 15 Apr 2026 - 7:31

score 604 · Answer 7 · 2026-04-15 19:16:27

604

Views

Gradient estimate for harmonic functions - Isn't a power missing on $N$?

Published on 15 Apr 2026 - 19:16

score 111 · Answer 8 · 2026-04-15 18:25:05

111

Views

Why is the exponent when working in $L^p$ spaces often dropped?

Published on 15 Apr 2026 - 18:25

score 676 · Answer 9 · 2026-04-12 10:33:43

676

Views

Prove functions in L1 space are Uniformly Continuous

Published on 12 Apr 2026 - 10:33

score 44 · Answer 10 · 2026-04-16 23:08:32

44

Views

Meaning of uniformly continuous in a function $K:L^p \rightarrow L^p$

Published on 16 Apr 2026 - 23:08

score 78 · Answer 11 · 2026-05-05 09:41:26

78

Views

Converse of density theorem for $L^1(\Omega)$

Published on 05 May 2026 - 9:41

score 76 · Answer 12 · 2026-04-16 01:32:18

76

Views

Proving limit of ratio of $L^p$ norms tends to $L^\infty$ norm

Published on 16 Apr 2026 - 1:32

score 1.6k · Answer 13 · 2026-04-14 18:09:57

1.6k

Views

Prove that dual space of $\ell^1$ is $\ell^{\infty}$

Published on 14 Apr 2026 - 18:09

score 219 · Answer 14 · 2026-04-11 03:53:16

219

Views

Dual spaces, Am I doing right?

Published on 11 Apr 2026 - 3:53

score 80 · Answer 15 · 2026-04-14 16:34:41

80

Views

Homeomorphism with Hilbert Cube

Published on 14 Apr 2026 - 16:34

List Question

Example of a bounded linear functional on $L^p$ space that is not trivially the dual of an $L^q$ function

Prove that a convolution product $(f\ast g)(x)$, with $f,g\in\mathcal{L}^2(\mathbb{R})$, goes to $0$ as $|x|$ goes to $\infty$.

Folland Question 6.4 trouble with estimating norm

Convergence of $h^{1-p}(f(x+h)-f(x))^{p}$ when $f$ is absolutely continuous and $f' \in L^{p}$

l2 compact operator

If $u(x):=\int_{x_0}^x v(t)\;dt$, then $u$ locally absolutely continuous.

Gradient estimate for harmonic functions - Isn't a power missing on $N$?

Why is the exponent when working in $L^p$ spaces often dropped?

Prove functions in L1 space are Uniformly Continuous

Meaning of uniformly continuous in a function $K:L^p \rightarrow L^p$

Converse of density theorem for $L^1(\Omega)$

Proving limit of ratio of $L^p$ norms tends to $L^\infty$ norm

Prove that dual space of $\ell^1$ is $\ell^{\infty}$

Dual spaces, Am I doing right?

Homeomorphism with Hilbert Cube

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