List questions from lp-spaces

Published on 14 Apr 2026 - 1:26

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Does the sequence $(\sqrt{n} \cdot 1_{[0, 1/n]})_n$ converge weakly in $L^2$?

Published on 16 Apr 2026 - 2:11

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Schwartz class dense in $L^2$, reference

Published on 14 Apr 2026 - 8:21

88

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Show that $||\hat{f}||_{\infty}=||f||_1$

Published on 16 Apr 2026 - 10:22

3.1k

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Voronoi diagram boundaries with Manhattan distance

Published on 15 Apr 2026 - 5:45

3.4k

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$L^p$ submartingale convergence theorem

Published on 14 Apr 2026 - 3:06

216

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Show strong but not norm convergence on $L^p$

Published on 13 Apr 2026 - 2:47

50

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Convergence in $L^p(U)$ of smooth functions acted on by a $C^1$ function with $|U|<\infty$

Published on 16 Apr 2026 - 3:53

224

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Limits of the p-norm

Published on 12 Apr 2026 - 11:08

170

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Mistake in reasoning about Sobolev spaces

Published on 13 Apr 2026 - 13:50

51

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Show that limit of integrals of sequence of orthonormal functions in $L^2([0,2\pi])$ goes to $0$.

Published on 14 Apr 2026 - 22:28

111

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Weakly convergent but not strongly convergent sequence in $L^2(\Bbb R^n)$.

Published on 17 Apr 2026 - 15:26

44

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Every translation of $f$ has no radial part

Published on 17 Apr 2026 - 0:34

73

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An equivalence related to determining the point spectrum of multiplication operator

Published on 12 Apr 2026 - 23:29

128

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norm in $L^2$ and $l^2$

Published on 14 Apr 2026 - 1:57

List Question

Is it true that $\|f\|_p\le c\|f\|_r$ when $r<p$?

Does the sequence $(\sqrt{n} \cdot 1_{[0, 1/n]})_n$ converge weakly in $L^2$?

Schwartz class dense in $L^2$, reference

Show that $||\hat{f}||_{\infty}=||f||_1$

Voronoi diagram boundaries with Manhattan distance

$L^p$ submartingale convergence theorem

Show strong but not norm convergence on $L^p$

Convergence in $L^p(U)$ of smooth functions acted on by a $C^1$ function with $|U|<\infty$

Limits of the p-norm

Mistake in reasoning about Sobolev spaces

Show that limit of integrals of sequence of orthonormal functions in $L^2([0,2\pi])$ goes to $0$.

Weakly convergent but not strongly convergent sequence in $L^2(\Bbb R^n)$.

Every translation of $f$ has no radial part

An equivalence related to determining the point spectrum of multiplication operator

norm in $L^2$ and $l^2$

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