List questions from lp-spaces

Published on 28 Mar 2026 - 15:26

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Projection of a $L^2$ function over a set of constant functions

Published on 25 Mar 2026 - 14:39

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Find the orthogonal complement of a subset of $L^2$

Published on 28 Mar 2026 - 15:25

57

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Which convergence when discussing density in $L^p$?

Published on 28 Dec 2018 - 21:11

47

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Does this norm have a specific name? References?

Published on 29 Dec 2018 - 21:39

907

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Dual of a subspace

Published on 25 Mar 2026 - 16:12

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$L(V,\mathbb{R})$ with $\|\cdot\|_1$ complete?

Published on 30 Dec 2018 - 13:16

859

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Bounded sequence in $L^\infty$ which converges in $L^1$

Published on 23 Feb 2026 - 12:31

40

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Is the supremum of $\int_{B(y,r)}\lvert u\rvert^{p^\ast}$ where $u\in W_0^{1,p}$ attained inside an open set?

Published on 29 Mar 2026 - 7:00

348

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A type of reverse Holder inequality

Published on 30 Dec 2018 - 20:44

127

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Is the set of sequences $(x_n)$ in $\ell^1$ such that $|x_n|\leqslant\frac1n$ for every $n$, compact in $\ell^1$?

Published on 30 Dec 2018 - 21:10

42

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Showing $\mathbb{R}^p\ni t \mapsto f_t \in L_\infty(\mathbb{R}^p, \mathcal B_p, \lambda_p, \mathbb{C})$ is not continuous

Published on 31 Dec 2018 - 14:06

59

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Function in $L^2$ that doesn't vanishing

Published on 25 Mar 2026 - 1:32

67

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For which values of $c$ is the function $f(x)$ in $W^{1,p}_{\mathrm{loc}} (\mathbb{R})$?

Published on 29 Mar 2026 - 8:44

48

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Find $f\in L^p(0,1)$, but $f\notin L^q(0,1)$, $p < q$

Published on 28 Mar 2026 - 1:07

List Question

Does Weak Convergence in $W^{1,2}$ imply weak convergence in $W^{1,4}$

Projection of a $L^2$ function over a set of constant functions

Find the orthogonal complement of a subset of $L^2$

Which convergence when discussing density in $L^p$?

Does this norm have a specific name? References?

Dual of a subspace

$L(V,\mathbb{R})$ with $\|\cdot\|_1$ complete?

Bounded sequence in $L^\infty$ which converges in $L^1$

Is the supremum of $\int_{B(y,r)}\lvert u\rvert^{p^\ast}$ where $u\in W_0^{1,p}$ attained inside an open set?

A type of reverse Holder inequality

Is the set of sequences $(x_n)$ in $\ell^1$ such that $|x_n|\leqslant\frac1n$ for every $n$, compact in $\ell^1$?

Showing $\mathbb{R}^p\ni t \mapsto f_t \in L_\infty(\mathbb{R}^p, \mathcal B_p, \lambda_p, \mathbb{C})$ is not continuous

Function in $L^2$ that doesn't vanishing

For which values of $c$ is the function $f(x)$ in $W^{1,p}_{\mathrm{loc}} (\mathbb{R})$?

Find $f\in L^p(0,1)$, but $f\notin L^q(0,1)$, $p < q$

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