List questions from lp-spaces

Published on 14 Aug 2019 - 8:00

165

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Determine the orthogonal projection of $L^2$ onto $\left\{f\in L^2:\int f=0\right\}$

Published on 27 Mar 2026 - 17:53

39

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$L^{2}$ spaces, bounding the measure of a set

Published on 18 Aug 2019 - 18:14

104

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$\mathrm{d}\mu(x) = \mathrm{d}\lambda(x)/x$, $\lambda$ is Lebesgue. Is $L^{\infty}([0,1],\lambda) = L^{\infty}([0,1],\mu)$?

Published on 26 Mar 2026 - 9:29

382

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Is the inclusion of schwartz space on $L^{p}$ continous

Published on 25 Mar 2026 - 20:15

302

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If $L^1$ average of $f$ is smaller than $t^2$ then $f=0$ a.e.

Published on 20 Aug 2019 - 8:15

75

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Can we approximate elements in $L^2$ via smooth maps while preserving a pointwise constraint on the derivatives?

Published on 25 Mar 2026 - 19:02

695

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No bounded surjective linear map $L^{\infty} \to L^1$

Published on 20 Aug 2019 - 17:56

30

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Characterization of $L_p(\mu)$ and $\mathcal{L}_{p,1+}$ spaces

Published on 29 Mar 2026 - 20:23

107

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How to prove that Lp norm exists?

Published on 22 Aug 2019 - 0:19

371

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Showing a set is closed in a Hilbert space

Published on 30 Mar 2026 - 15:02

1.3k

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Comparing $L^p$-norms of a function for two different values of $p$.

Published on 25 Mar 2026 - 23:37

57

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$f_n(x) \rightharpoonup0$ in $L^1(\mathbb{R})$ where $f_n(x) = f(-x+n^3)$

Published on 23 Feb 2026 - 19:23

53

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Difference between $L^2$ and $L_{\sigma}^{2}$

Published on 25 Mar 2026 - 19:00

23

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If $\int g(x)(h(x+a)-h(x)dx=0$ $h\in L^\infty$, $g\in L^1$ then $h$ constant.

Published on 28 Mar 2026 - 19:30

List Question

Convergence of measure topology

Determine the orthogonal projection of $L^2$ onto $\left\{f\in L^2:\int f=0\right\}$

$L^{2}$ spaces, bounding the measure of a set

$\mathrm{d}\mu(x) = \mathrm{d}\lambda(x)/x$, $\lambda$ is Lebesgue. Is $L^{\infty}([0,1],\lambda) = L^{\infty}([0,1],\mu)$?

Is the inclusion of schwartz space on $L^{p}$ continous

If $L^1$ average of $f$ is smaller than $t^2$ then $f=0$ a.e.

Can we approximate elements in $L^2$ via smooth maps while preserving a pointwise constraint on the derivatives?

No bounded surjective linear map $L^{\infty} \to L^1$

Characterization of $L_p(\mu)$ and $\mathcal{L}_{p,1+}$ spaces

How to prove that Lp norm exists?

Showing a set is closed in a Hilbert space

Comparing $L^p$-norms of a function for two different values of $p$.

$f_n(x) \rightharpoonup0$ in $L^1(\mathbb{R})$ where $f_n(x) = f(-x+n^3)$

Difference between $L^2$ and $L_{\sigma}^{2}$

If $\int g(x)(h(x+a)-h(x)dx=0$ $h\in L^\infty$, $g\in L^1$ then $h$ constant.

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