List questions from lp-spaces

Published on 13 Apr 2026 - 3:46

44

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$\| u \|_{W^{k,p}(K)} \leq c$ for every $K \subset U$ implies $u \in W^{k,p}(U)$

Published on 28 Mar 2026 - 13:41

36

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A question about convergence in $L_1$

Published on 12 Apr 2026 - 15:54

1.2k

Views

Bounded martingale that does not converge in $L^1$

Published on 13 Apr 2026 - 15:58

207

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Weak convergence in $L^q([0,1]) \subset L^p([0,1])$.

Published on 16 Apr 2026 - 0:46

297

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compactness of a set on L2(0,1)

Published on 15 Apr 2026 - 18:09

30

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Proving that the limit of an $L^p$ sequence is also $L^p$

Published on 16 Apr 2026 - 3:53

69

Views

Compactness for Orlicz spaces

Published on 25 Mar 2026 - 9:22

145

Views

functional analysis, Schwartz space, $L^p(\mathbb{R},\lambda)$

Published on 10 Apr 2026 - 17:05

228

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How to show that $\|f+g\|_p=\|f\|_p+\|g\|_p$ implies $f$ and $g$ are positively linearly dependent?

Published on 16 Apr 2026 - 17:45

472

Views

Proving that a subset is compact in $L^2(0,1)$

Published on 15 Apr 2026 - 13:58

48

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Find a function that has finite values for lower norm but becomes infinite

Published on 14 Apr 2026 - 5:20

29

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Find the lowest value for a lower norm subject to norm-2 being infinite

Published on 11 Apr 2026 - 19:24

128

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Bounded $p$-norm but unbounded $q$-norm for any $p < q$

Published on 14 Apr 2026 - 21:32

203

Views

Proof that $L^p(\mu)$ is complete in Rudin's book (RCA)

Published on 13 Apr 2026 - 2:18

List Question

Denseness of continuous functions with specific properties

$\| u \|_{W^{k,p}(K)} \leq c$ for every $K \subset U$ implies $u \in W^{k,p}(U)$

A question about convergence in $L_1$

Bounded martingale that does not converge in $L^1$

Weak convergence in $L^q([0,1]) \subset L^p([0,1])$.

compactness of a set on L2(0,1)

Proving that the limit of an $L^p$ sequence is also $L^p$

Compactness for Orlicz spaces

functional analysis, Schwartz space, $L^p(\mathbb{R},\lambda)$

How to show that $\|f+g\|_p=\|f\|_p+\|g\|_p$ implies $f$ and $g$ are positively linearly dependent?

Proving that a subset is compact in $L^2(0,1)$

Find a function that has finite values for lower norm but becomes infinite

Find the lowest value for a lower norm subject to norm-2 being infinite

Bounded $p$-norm but unbounded $q$-norm for any $p < q$

Proof that $L^p(\mu)$ is complete in Rudin's book (RCA)

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