Question

Explanation of a passage about a smooth approximation to $L^p$ function

score 134 · Answer 1 · 2026-03-29 07:28:36

134

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Explanation of a passage about a smooth approximation to $L^p$ function

Published on 29 Mar 2026 - 7:28

score 444 · Answer 2 · 2014-06-05 01:37:41

444

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Is $ L^{\infty} $ a direct limit or inverse limit of the directed system $ (L^p , i_{p}^q )_{p,q \in [1 , + \infty [ } $?

Published on 05 Jun 2014 - 1:37

score 140 · Answer 3 · 2026-03-28 04:53:15

140

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Find $\psi\in L^2$ so that the overlap $\langle \psi(x+\delta),\psi(x-\delta)\rangle$ is as small as possible

Published on 28 Mar 2026 - 4:53

score 151 · Answer 4 · 2026-03-30 04:56:36

151

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Continuity of $|.|$ in $W^{1,p}_0$

Published on 30 Mar 2026 - 4:56

score 43 · Answer 5 · 2014-06-09 10:02:33

43

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Showing a composition is in $L^2$

Published on 09 Jun 2014 - 10:02

score 99 · Answer 6 · 2014-06-10 12:33:54

99

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If $a_n \to a$ in $L^2$ and $F:\mathbb{R} \to \mathbb{R}$ is continuous, does $\int F(a_{n_j}) \to \int F(a)$?

Published on 10 Jun 2014 - 12:33

score 70 · Answer 7 · 2026-04-01 01:58:52

70

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Exercise on abstract integration

Published on 01 Apr 2026 - 1:58

score 195 · Answer 8 · 2026-03-26 04:36:28

195

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Reference for $f \in L^{p,\infty} \cap L^{q}$ then $f \in L^r$ for $p < r \leq q$

Published on 26 Mar 2026 - 4:36

score 163 · Answer 9 · 2026-03-30 04:53:32

163

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Sequence which does not admit weakly convergent subsequences

Published on 30 Mar 2026 - 4:53

score 358 · Answer 10 · 2026-03-31 07:57:20

358

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Inequality between Fourier coefficients implies inequality for $L^p$ norms on the circle

Published on 31 Mar 2026 - 7:57

score 84 · Answer 11 · 2014-06-13 11:08:16

84

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Rate of divergence of the integral of an $L^q$ function

Published on 13 Jun 2014 - 11:08

score 219 · Answer 12 · 2026-03-26 21:12:42

219

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Prove that the $p$-mean is an increasing function of $p$

Published on 26 Mar 2026 - 21:12

score 41 · Answer 13 · 2014-06-13 18:01:53

41

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Functional relation to be in $L^{p}$

Published on 13 Jun 2014 - 18:01

score 74 · Answer 14 · 2014-06-13 18:48:08

74

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The asymptotics of $\int_x^1 |f|$ as $x\to 0$ for a nonintegrable function with $\int_0^1|f|^p<\infty$, $0<p<1$

Published on 13 Jun 2014 - 18:48

score 216 · Answer 15 · 2026-03-31 06:28:41

216

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Isometric isomorphism between $\ell^{1}(\mathbb{R}^{3})$ and $\ell^{\infty}(\mathbb{R}^{3})$

Published on 31 Mar 2026 - 6:28

List Question

Explanation of a passage about a smooth approximation to $L^p$ function

Is $ L^{\infty} $ a direct limit or inverse limit of the directed system $ (L^p , i_{p}^q )_{p,q \in [1 , + \infty [ } $?

Find $\psi\in L^2$ so that the overlap $\langle \psi(x+\delta),\psi(x-\delta)\rangle$ is as small as possible

Continuity of $|.|$ in $W^{1,p}_0$

Showing a composition is in $L^2$

If $a_n \to a$ in $L^2$ and $F:\mathbb{R} \to \mathbb{R}$ is continuous, does $\int F(a_{n_j}) \to \int F(a)$?

Exercise on abstract integration

Reference for $f \in L^{p,\infty} \cap L^{q}$ then $f \in L^r$ for $p < r \leq q$

Sequence which does not admit weakly convergent subsequences

Inequality between Fourier coefficients implies inequality for $L^p$ norms on the circle

Rate of divergence of the integral of an $L^q$ function

Prove that the $p$-mean is an increasing function of $p$

Functional relation to be in $L^{p}$

The asymptotics of $\int_x^1 |f|$ as $x\to 0$ for a nonintegrable function with $\int_0^1|f|^p<\infty$, $0<p<1$

Isometric isomorphism between $\ell^{1}(\mathbb{R}^{3})$ and $\ell^{\infty}(\mathbb{R}^{3})$

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