List questions from lp-spaces

Published on 15 Apr 2026 - 22:12

223

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For $0<p<1$ showing $\Big(\int_\Omega |f|^pd\mu\Big)^{1/p}\leq \frac{1}{R_0} + \Big(\int_\Omega |f_{R_0}|^p\Big)^{1/p} $

Published on 17 Apr 2026 - 5:40

454

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When do $L^p$ and $L^q$ contain the same functions?

Published on 12 Apr 2026 - 19:40

37

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sufficient conditions for integrability of a bivariate function

Published on 10 Apr 2026 - 9:53

108

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Example of such family of functions in $L^{p}(\mathbb{R})$?

Published on 15 Apr 2026 - 10:49

410

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Does $L^2$ convergence imply convergence of integrals?

Published on 12 Apr 2026 - 17:28

211

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$L^p$ space: measure theory

Published on 14 Apr 2026 - 1:36

59

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lp spaces, linear functionals

Published on 13 Apr 2026 - 0:53

164

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weak and strong $L^p$ convergence

Published on 12 Apr 2026 - 0:03

103

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No weak derivative in singularity

Published on 05 May 2026 - 14:40

22

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Let $\Gamma _g(f)=\int_{\mathbb R}fg$. Prove that $\|\Gamma _g\|=\|g\|_{L^{p'}}$.

Published on 16 Apr 2026 - 6:29

29

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Compute norm for a continuous function.

Published on 11 Apr 2026 - 11:26

67

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Prove $\|x_1 + \cdots + x_m\|_p \leq m^{\text{max}\{0, 1/p - 1\}}(\|x_1\|_p + \cdots + \|x_m\|_p)$ for $p \in (0, \infty), x_i \in \mathbb{C}^n$.

Published on 17 Apr 2026 - 14:39

34

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rearrangement of series in $\ell^p$ space

Published on 12 Apr 2026 - 19:05

42

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Show a series in $\ell^{\infty}$ converges to a point in $c_0$

Published on 16 Apr 2026 - 3:05

List Question

Showing weak convergence of a sequence in $L^p(R)$

For $0<p<1$ showing $\Big(\int_\Omega |f|^pd\mu\Big)^{1/p}\leq \frac{1}{R_0} + \Big(\int_\Omega |f_{R_0}|^p\Big)^{1/p} $

When do $L^p$ and $L^q$ contain the same functions?

sufficient conditions for integrability of a bivariate function

Example of such family of functions in $L^{p}(\mathbb{R})$?

Does $L^2$ convergence imply convergence of integrals?

$L^p$ space: measure theory

lp spaces, linear functionals

weak and strong $L^p$ convergence

No weak derivative in singularity

Let $\Gamma _g(f)=\int_{\mathbb R}fg$. Prove that $\|\Gamma _g\|=\|g\|_{L^{p'}}$.

Compute norm for a continuous function.

Prove $\|x_1 + \cdots + x_m\|_p \leq m^{\text{max}\{0, 1/p - 1\}}(\|x_1\|_p + \cdots + \|x_m\|_p)$ for $p \in (0, \infty), x_i \in \mathbb{C}^n$.

rearrangement of series in $\ell^p$ space

Show a series in $\ell^{\infty}$ converges to a point in $c_0$

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