Question

What motivated mathematicians to realize that $L^p \simeq (L^q)^*$?

score 99 · Answer 1 · 2017-04-08 16:34:59

99

Views

What motivated mathematicians to realize that $L^p \simeq (L^q)^*$?

Published on 08 Apr 2017 - 16:34

score 33 · Answer 2 · 2017-04-09 02:52:48

33

Views

Example of a sequence of function $f_n$ converging pointwise to $f$ in $\Bbb R$ but not converging in $L^p(E)$.

Published on 09 Apr 2017 - 2:52

score 86 · Answer 3 · 2026-04-01 08:53:49

86

Views

A name for this statistical approximation?

Published on 01 Apr 2026 - 8:53

score 104 · Answer 4 · 2026-03-25 08:13:38

104

Views

About functions in fractional Sobolev spaces $W^{s,p}(\mathbb{R})$ and $\lim_{x\rightarrow a^{+}}\int_{a}^{x}\frac{f(y)}{(x-y)^{s}}dy=0$

Published on 25 Mar 2026 - 8:13

score 163 · Answer 5 · 2023-02-01 19:01:08

163

Views

If $f_n$ converges to $f$ in $L^p$ then does $f_n^2$ converge to $f^2$?

Published on 01 Feb 2023 - 19:01

score 80 · Answer 6 · 2026-03-25 22:04:22

80

Views

Convergence of sums in $\ell^p \implies \ell^{p-\epsilon}$

Published on 25 Mar 2026 - 22:04

score 33 · Answer 7 · 2023-02-02 20:39:15

33

Views

Showing that $\ell^{2}$ is contained in $c_{0}$.

Published on 02 Feb 2023 - 20:39

score 40 · Answer 8 · 2023-02-03 19:29:03

40

Views

Understanding two representations of the inner product between elements of the form $f:\prod_k H_k\to\mathbb{C}$ for Hilbert spaces $H_k$ (e.g. $L^2$)

Published on 03 Feb 2023 - 19:29

score 55 · Answer 9 · 2023-02-05 02:57:39

55

Views

Showing that linear map is bounded for $ q = 1.$

Published on 05 Feb 2023 - 2:57

score 42 · Answer 10 · 2023-02-05 18:48:09

42

Views

Relationship between $\ell^p$-norm and $L^p$-norm

Published on 05 Feb 2023 - 18:48

score 75 · Answer 11 · 2026-04-01 11:43:32

75

Views

Tempered distribution in Sobolev sapce

Published on 01 Apr 2026 - 11:43

score 24 · Answer 12 · 2023-02-10 09:07:37

24

Views

Counterexample of $L^p(E)$ space when $m(E) = \infty$

Published on 10 Feb 2023 - 9:07

score 254 · Answer 13 · 2026-04-07 11:34:27

254

Views

Can we bound the L1 distance between densities by Wasserstein distance of measures

Published on 07 Apr 2026 - 11:34

score 91 · Answer 14 · 2023-02-10 15:51:09

91

Views

Small exercise on Minkowski inequality

Published on 10 Feb 2023 - 15:51

score 311 · Answer 15 · 2023-02-10 18:29:11

311

Views

When does coordinate-wise differentiability imply $\ell^{p}$ differentiability?

Published on 10 Feb 2023 - 18:29

List Question

What motivated mathematicians to realize that $L^p \simeq (L^q)^*$?

Example of a sequence of function $f_n$ converging pointwise to $f$ in $\Bbb R$ but not converging in $L^p(E)$.

A name for this statistical approximation?

About functions in fractional Sobolev spaces $W^{s,p}(\mathbb{R})$ and $\lim_{x\rightarrow a^{+}}\int_{a}^{x}\frac{f(y)}{(x-y)^{s}}dy=0$

If $f_n$ converges to $f$ in $L^p$ then does $f_n^2$ converge to $f^2$?

Convergence of sums in $\ell^p \implies \ell^{p-\epsilon}$

Showing that $\ell^{2}$ is contained in $c_{0}$.

Understanding two representations of the inner product between elements of the form $f:\prod_k H_k\to\mathbb{C}$ for Hilbert spaces $H_k$ (e.g. $L^2$)

Showing that linear map is bounded for $ q = 1.$

Relationship between $\ell^p$-norm and $L^p$-norm

Tempered distribution in Sobolev sapce

Counterexample of $L^p(E)$ space when $m(E) = \infty$

Can we bound the L1 distance between densities by Wasserstein distance of measures

Small exercise on Minkowski inequality

When does coordinate-wise differentiability imply $\ell^{p}$ differentiability?

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