List questions from lp-spaces

Published on 11 Apr 2026 - 20:35

103

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Show that $g_n(x)g_m(y)$ forms an orthonormal basis for $L^2(\Omega \times \Omega)$ when $g_n$ is an orthonormal basis of $L^2(\Omega)$

Published on 04 Feb 2024 - 11:10

92

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Showing if $f' \in L^2([1,\infty),m)$, then $\frac{f(x)}{x} \in L^2([1,\infty),m)$

Published on 04 Feb 2024 - 23:35

66

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$L^p_x$ norms of $f(x, x+y)$

Published on 27 Mar 2026 - 18:28

65

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Functions in $L^p$ have zero lim inf.

Published on 06 Feb 2024 - 0:32

39

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Adjoint operator and random variable

Published on 26 Mar 2026 - 8:04

52

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A lemma on the $L_p$ estimates

Published on 07 Feb 2024 - 0:24

142

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$W^{1,p}(\Omega)$ estimates of solutions of elliptic equation

Published on 27 Mar 2026 - 1:00

41

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$p$-integrability of a certain Bessel function

Published on 11 Apr 2026 - 23:49

41

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Trying to understand the proof for the criterion of compactness in $l_p$ space

Published on 12 Apr 2026 - 2:32

237

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$L^1- L^\infty$ estimate for the semi group of wave equations

Published on 12 Feb 2024 - 11:44

43

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Why is it bad to translate from Lp norm to priors?

Published on 12 Feb 2024 - 23:22

141

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Does $\sin (nx)$ converge in $L^2$?

Published on 11 Apr 2026 - 19:07

67

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Equivalence of two forms of the Marcinkiewicz interpolation theorem

Published on 04 Apr 2026 - 12:09

35

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Sequence in $\ell_p$ spaces

Published on 07 Apr 2026 - 21:10

List Question

Ratio involving $l_p$ norms

Show that $g_n(x)g_m(y)$ forms an orthonormal basis for $L^2(\Omega \times \Omega)$ when $g_n$ is an orthonormal basis of $L^2(\Omega)$

Showing if $f' \in L^2([1,\infty),m)$, then $\frac{f(x)}{x} \in L^2([1,\infty),m)$

$L^p_x$ norms of $f(x, x+y)$

Functions in $L^p$ have zero lim inf.

Adjoint operator and random variable

A lemma on the $L_p$ estimates

$W^{1,p}(\Omega)$ estimates of solutions of elliptic equation

$p$-integrability of a certain Bessel function

Trying to understand the proof for the criterion of compactness in $l_p$ space

$L^1- L^\infty$ estimate for the semi group of wave equations

Why is it bad to translate from Lp norm to priors?

Does $\sin (nx)$ converge in $L^2$?

Equivalence of two forms of the Marcinkiewicz interpolation theorem

Sequence in $\ell_p$ spaces

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