List questions from lp-spaces

Published on 24 Mar 2026 - 23:55

124

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Completeness of $\ell^\infty$

Published on 25 Mar 2026 - 12:16

321

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Proving that a function related to the Fourier transform of the unit ball is in $L^1(\mathbb{R}^3)$

Published on 15 Jun 2018 - 5:55

67

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I don't understand this application of Holder's inequality

Published on 25 Mar 2026 - 6:05

423

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Essential range of a function is closed

Published on 16 Jun 2018 - 20:47

56

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Which convergence can be deduced for $\sqrt{X_n}$?

Published on 17 Jun 2018 - 8:17

270

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Prove that $(T f)(x) = x^{-1/p}\int_0^x f(t)dt$ is continuous.

Published on 19 Jun 2018 - 10:33

114

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Is $L^p\cap L^q$ a real intersection?

Published on 19 Jun 2018 - 11:07

78

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$x=\left (1,\frac{1}{\sqrt{2}\ln(2)},\frac{1}{\sqrt{3}\ln(3)},\dots,\frac{1}{\sqrt{n}\ln(n)},\dots\right)\in l_p$?

Published on 20 Jun 2018 - 12:42

641

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Relation between convolution and $L^p$ norms

Published on 24 Mar 2026 - 23:59

209

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The properties of $c_{00}$.

Published on 21 Jun 2018 - 16:01

74

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Prove that a functional in $L^2(0, \pi)$ is bounded

Published on 21 Jun 2018 - 17:30

205

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1d-heat equation $L_{\infty}$

Published on 25 Mar 2026 - 6:09

75

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If $u_{n} \rightarrow u$ in $L^{p}$ and $v_{n} \rightarrow v$ in $L^{q}$, can I conclude that $\int u_{n}^{p}v_{n}^{q}$ converges?

Published on 26 Jun 2018 - 3:41

66

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Convolution operator in $L^p$

Published on 25 Mar 2026 - 17:35

List Question

Finding a function $f\in L^p \setminus L^q$ for $0<p<q<\infty$

Completeness of $\ell^\infty$

Proving that a function related to the Fourier transform of the unit ball is in $L^1(\mathbb{R}^3)$

I don't understand this application of Holder's inequality

Essential range of a function is closed

Which convergence can be deduced for $\sqrt{X_n}$?

Prove that $(T f)(x) = x^{-1/p}\int_0^x f(t)dt$ is continuous.

Is $L^p\cap L^q$ a real intersection?

$x=\left (1,\frac{1}{\sqrt{2}\ln(2)},\frac{1}{\sqrt{3}\ln(3)},\dots,\frac{1}{\sqrt{n}\ln(n)},\dots\right)\in l_p$?

Relation between convolution and $L^p$ norms

The properties of $c_{00}$.

Prove that a functional in $L^2(0, \pi)$ is bounded

1d-heat equation $L_{\infty}$

If $u_{n} \rightarrow u$ in $L^{p}$ and $v_{n} \rightarrow v$ in $L^{q}$, can I conclude that $\int u_{n}^{p}v_{n}^{q}$ converges?

Convolution operator in $L^p$

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