List questions from lp-spaces

Published on 10 Apr 2026 - 19:46

48

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On denseness of a subspace of trigonometric polynomials in $L^1(\mathbb T).$

Published on 16 Apr 2026 - 7:14

41

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On convergence of the same sequence under two different norms.

Published on 14 Apr 2026 - 13:18

229

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Is $\ell^p$ a subset of $c_0$ for all finite $p$?

Published on 15 Apr 2026 - 11:34

148

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Why is the factor in Doob‘s classical $L^p$ inequality optimal?

Published on 13 Apr 2026 - 21:43

69

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Are the translates of a function in $H^1(\mathbb{R}^2)$ bounded by a function with finite integral over some compact set?

Published on 14 May 2026 - 14:23

214

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Check whether operator $T: L^1[0,1] \to L[0,1]$ is compact.

Published on 14 Apr 2026 - 23:19

105

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Inverse of $\Phi(f) =\operatorname{sgn}(f)\lvert f\rvert^{1/p}$ is continuous from $L^p(E)$ to $L^1(E)$

Published on 16 Apr 2026 - 16:54

42

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Closed subset in different norms

Published on 11 Apr 2026 - 0:41

112

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Funny consequence of Hölder Inequality

Published on 14 Apr 2026 - 22:55

126

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Question about the norm on L^p space

Published on 11 Apr 2026 - 16:12

125

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Let $f \in L^1 (\mathbb{R}), f_n(x):=f(x-\frac{1}{n})$. Prove that $f_n$ converges to $f$ in $L^1(\mathbb{R})$.

Published on 17 Apr 2026 - 15:45

387

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convolution continuous if $f,g \in L^2(\mathbb{R})$

Published on 16 Apr 2026 - 4:54

53

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$\int_E f_ng \to \int_E fg$ implies $\{\|f_n\|_p\}$ is uniformly bounded

Published on 13 Apr 2026 - 19:07

60

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Martingale Convergence under equivalent probability measures

Published on 13 Apr 2026 - 23:46

List Question

What is the Double and Triple Dual of $\ell^\infty$

On denseness of a subspace of trigonometric polynomials in $L^1(\mathbb T).$

On convergence of the same sequence under two different norms.

Is $\ell^p$ a subset of $c_0$ for all finite $p$?

Why is the factor in Doob‘s classical $L^p$ inequality optimal?

Are the translates of a function in $H^1(\mathbb{R}^2)$ bounded by a function with finite integral over some compact set?

Check whether operator $T: L^1[0,1] \to L[0,1]$ is compact.

Inverse of $\Phi(f) =\operatorname{sgn}(f)\lvert f\rvert^{1/p}$ is continuous from $L^p(E)$ to $L^1(E)$

Closed subset in different norms

Funny consequence of Hölder Inequality

Question about the norm on L^p space

Let $f \in L^1 (\mathbb{R}), f_n(x):=f(x-\frac{1}{n})$. Prove that $f_n$ converges to $f$ in $L^1(\mathbb{R})$.

convolution continuous if $f,g \in L^2(\mathbb{R})$

$\int_E f_ng \to \int_E fg$ implies $\{\|f_n\|_p\}$ is uniformly bounded

Martingale Convergence under equivalent probability measures

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