List questions from lp-spaces

Published on 21 Jul 2020 - 11:51

242

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A detail in proving that a sequence of uniformly integrable random variables converges weakly.

Published on 21 Jul 2020 - 17:43

34

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Extending an operator from $C([0,1])$ to $L^2([0,1])$

Published on 21 Jul 2020 - 21:33

83

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$L^p$ Approximation of a $L^p$ function on $\Bbb R$ for $1\leq p<\infty$

Published on 22 Jul 2020 - 14:44

103

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Showing that $\|f\|_{\infty}\leq \liminf_{p\to \infty}\|f\|_p$.

Published on 23 Jul 2020 - 2:51

310

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A question for a measurable function $g$ on a finite measure space such that $fg\in L^p$ for all $f\in L^p$

Published on 23 Jul 2020 - 6:53

295

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Proof Check: Multiplication operator on $L^{p}(\mathbb R^{d})$ is closed

Published on 23 Jul 2020 - 12:58

213

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Time continuity of the function in L1 norm i.e. $C([0,T];L^1) $

Published on 25 Mar 2026 - 8:09

26

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$w^-w^$-closedness of non-linear operator on $L^{\infty}$

Published on 24 Jul 2020 - 9:47

34

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$L_2$ convergence maintains the sign

Published on 24 Jul 2020 - 12:00

968

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Fourier coefficients of $L^{\infty}$ function

Published on 05 Apr 2026 - 20:12

27

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Does function $f(x,y,z) = \frac{1}{\|\mathbf{x}\|}+\sin(x^2y)\cos(z-7)$ belong to space $L^k(B)$ for $k = 1, 2, 3, 4$?

Published on 25 Jul 2020 - 17:18

140

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Why does the irreflexivity of $L^1$ follow from $(L^1)'' \subsetneq L^1$?

Published on 23 Feb 2026 - 4:41

33

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$g_n = m(E_n)^{\frac{-1}{q}}\chi_{E_n}$. Show $\int fg_n \rightarrow 0$

Published on 26 Jul 2020 - 17:09

90

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Does weak convergence of functions on periodic domains implies strong convergence?

Published on 30 Mar 2026 - 20:42

List Question

How to show given function in $L^r(\Omega)$?

A detail in proving that a sequence of uniformly integrable random variables converges weakly.

Extending an operator from $C([0,1])$ to $L^2([0,1])$

$L^p$ Approximation of a $L^p$ function on $\Bbb R$ for $1\leq p<\infty$

Showing that $\|f\|_{\infty}\leq \liminf_{p\to \infty}\|f\|_p$.

A question for a measurable function $g$ on a finite measure space such that $fg\in L^p$ for all $f\in L^p$

Proof Check: Multiplication operator on $L^{p}(\mathbb R^{d})$ is closed

Time continuity of the function in L1 norm i.e. $C([0,T];L^1) $

$w^-w^$-closedness of non-linear operator on $L^{\infty}$

$L_2$ convergence maintains the sign

Fourier coefficients of $L^{\infty}$ function

Does function $f(x,y,z) = \frac{1}{\|\mathbf{x}\|}+\sin(x^2y)\cos(z-7)$ belong to space $L^k(B)$ for $k = 1, 2, 3, 4$?

Why does the irreflexivity of $L^1$ follow from $(L^1)'' \subsetneq L^1$?

$g_n = m(E_n)^{\frac{-1}{q}}\chi_{E_n}$. Show $\int fg_n \rightarrow 0$

Does weak convergence of functions on periodic domains implies strong convergence?

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