List questions from lp-spaces

Published on 13 Apr 2026 - 11:10

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Suppose $E \subset \mathbb{R}$ has infinite measure, and $f\in L^1(E)$, Is this true that $f \in L^{\infty}(E)$ necessarily?

Published on 14 Apr 2026 - 18:06

72

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Prove that if $f,g \in L^1(-\infty,+\infty)$ and $h(x)=\int^{+\infty}_{-\infty}f(x-e^y)g(y)dy$ then $h \in L^1(-\infty,+\infty)$

Published on 16 Apr 2026 - 15:05

90

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property of a given subset $ A $ of $\mathit{l}^2 $

Published on 11 Apr 2026 - 22:21

83

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Convergence in $L^{p_1}$ and $L^{p_2}$

Published on 13 Apr 2026 - 23:39

275

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Translating an integrable function creates a sequence that converges to $0$ almost everywhere

Published on 12 Apr 2026 - 21:16

1.2k

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Show that for any $f\in L^1$ and $g \in L^p(\mathbb R)$, $\lVert f ∗ g\rVert_p \leqslant \lVert f\rVert_1\lVert g\rVert_p$.

Published on 16 Apr 2026 - 11:30

176

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How Lp spaces relate regarding convergence

Published on 09 Apr 2026 - 21:42

2.9k

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$L^p$ spaces and counting measure

Published on 10 Apr 2026 - 11:38

267

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Integral convergence and weak convergence

Published on 24 Apr 2026 - 21:24

4k

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What does the $L^p$ norm tend to as $p\to 0$?

Published on 13 Apr 2026 - 13:29

5.6k

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Weak convergence implies uniform boundedness

Published on 16 Apr 2026 - 8:45

54

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A basic question about $W^{1,1}(\Omega)$

Published on 24 Apr 2026 - 23:07

92

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Relation between convergences in $L^{p}$ for probability spaces.

Published on 15 Apr 2026 - 3:02

246

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Laplace Transform of $L^{2}$ Function.

Published on 14 Apr 2026 - 0:42

List Question

Continuous functions vanishing at infinity is always integrable?

Suppose $E \subset \mathbb{R}$ has infinite measure, and $f\in L^1(E)$, Is this true that $f \in L^{\infty}(E)$ necessarily?

Prove that if $f,g \in L^1(-\infty,+\infty)$ and $h(x)=\int^{+\infty}_{-\infty}f(x-e^y)g(y)dy$ then $h \in L^1(-\infty,+\infty)$

property of a given subset $ A $ of $\mathit{l}^2 $

Convergence in $L^{p_1}$ and $L^{p_2}$

Translating an integrable function creates a sequence that converges to $0$ almost everywhere

Show that for any $f\in L^1$ and $g \in L^p(\mathbb R)$, $\lVert f ∗ g\rVert_p \leqslant \lVert f\rVert_1\lVert g\rVert_p$.

How Lp spaces relate regarding convergence

$L^p$ spaces and counting measure

Integral convergence and weak convergence

What does the $L^p$ norm tend to as $p\to 0$?

Weak convergence implies uniform boundedness

A basic question about $W^{1,1}(\Omega)$

Relation between convergences in $L^{p}$ for probability spaces.

Laplace Transform of $L^{2}$ Function.

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