List questions from lp-spaces

Published on 29 Mar 2026 - 6:28

152

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Weak Convergence in the Space $L_1$, Why So Special?

Published on 20 May 2020 - 18:08

71

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$c_{00}$ and the $\ell^2$-norm

Published on 22 May 2020 - 1:24

107

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If $f\in L^{p_0}[0,1]$, $p_0$ is a given number big enough. Prove: $\lim_{p \to 0+}\Vert f\Vert_p=e^{\int_0^1 \ln\vert f(x)\vert dx}.$

Published on 22 May 2020 - 14:24

195

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Find the values of the parameter $\lambda$ for which $\mathop{\lim}\limits_{\epsilon\to 0+} \frac1{\epsilon^\lambda} \int_0^\epsilon f = 0$

Published on 23 May 2020 - 4:18

115

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Generalization of Kolmogorov precompactness criterion

Published on 05 Apr 2026 - 21:30

32

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Particular property of $p$-norm with $1<p\le 2$

Published on 23 May 2020 - 10:44

70

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Linear operator on $\ell^{\infty}$ is not surjective – well-definition of inverse operator

Published on 23 May 2020 - 21:31

138

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Fourier transform of $(1/\sqrt{x}) \mathbb{1}_{[0,1]}$

Published on 01 Apr 2026 - 23:08

220

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Schwarz space $S(\mathbb{R})$ is dense inside $L_p(\mathbb{R})$-spaces

Published on 26 Mar 2026 - 5:54

564

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Lp Space: an intuitive understanding.

Published on 26 May 2020 - 20:06

50

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Please define $\ell^2$ space and give some examples of its subspaces

Published on 28 May 2020 - 6:03

91

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Weak convergence in $L^p=L^p(\Omega,\mu)$

Published on 28 May 2020 - 13:11

129

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boundedness and convergence under integral implies weak convergence

Published on 28 May 2020 - 16:40

141

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Convergence in $L^p$ implies convergence in weighted $L^p$

Published on 29 May 2020 - 20:53

List Question

Approximation of functions mesurable w.r.t a generated $\sigma$-algebra.

Weak Convergence in the Space $L_1$, Why So Special?

$c_{00}$ and the $\ell^2$-norm

If $f\in L^{p_0}[0,1]$, $p_0$ is a given number big enough. Prove: $\lim_{p \to 0+}\Vert f\Vert_p=e^{\int_0^1 \ln\vert f(x)\vert dx}.$

Find the values of the parameter $\lambda$ for which $\mathop{\lim}\limits_{\epsilon\to 0+} \frac1{\epsilon^\lambda} \int_0^\epsilon f = 0$

Generalization of Kolmogorov precompactness criterion

Particular property of $p$-norm with $1<p\le 2$

Linear operator on $\ell^{\infty}$ is not surjective – well-definition of inverse operator

Fourier transform of $(1/\sqrt{x}) \mathbb{1}_{[0,1]}$

Schwarz space $S(\mathbb{R})$ is dense inside $L_p(\mathbb{R})$-spaces

Lp Space: an intuitive understanding.

Please define $\ell^2$ space and give some examples of its subspaces

Weak convergence in $L^p=L^p(\Omega,\mu)$

boundedness and convergence under integral implies weak convergence

Convergence in $L^p$ implies convergence in weighted $L^p$

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