List questions from lp-spaces

Published on 08 Apr 2026 - 21:24

123

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Compact matrix integral operator bound via its kernel

Published on 10 Apr 2026 - 7:45

80

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Understanding this integral from a measure theory perspective.

Published on 08 Apr 2026 - 9:28

131

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Completeness of $l_1 ^\infty$

Published on 14 Apr 2026 - 14:51

119

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Property of functions: do there exist counterexamples?

Published on 11 Apr 2026 - 17:03

217

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Proving fact about shifts of $L^\infty$ functions

Published on 12 Apr 2026 - 0:46

1.2k

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How to prove that a Schwartz function belongs to $L^p$?

Published on 04 Apr 2026 - 0:59

59

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If $0<\mu(X)<\infty$ and $0<p<q< \infty$. Is $(\int_X |f|^p) ^\frac{1}{p}\leq \int_X |f|^q d\mu) ^\frac{1}{q}$ true?

Published on 17 Apr 2026 - 11:28

377

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$L^p$ convergence of infinitesimal generator

Published on 12 Nov 2015 - 10:04

815

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function $f\notin L^{\infty}(\Omega)$, but $f\in L^p(\Omega)$ for all $1\le p <\infty$

Published on 14 Apr 2026 - 21:53

216

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Does $L^p$ have a basis for which the Pythagorean identity with exponent $p$ holds?

Published on 13 Apr 2026 - 8:26

293

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exercise: dual of an Lp-space

Published on 28 Mar 2026 - 14:05

88

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Convolution with imaginary Gaussian cannot be a $(p, p)$ operator unless $p=2$

Published on 14 Apr 2026 - 12:34

21.6k

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Uniform Convergence Implies $L^2$ Convergence and $L^2$ Convergence Implies $L^1$ Convergence

Published on 16 Apr 2026 - 0:41

300

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Normalize a function and a measure so that the $L^p$ norm is $1$ for two values of $p$

Published on 15 Apr 2026 - 13:18

List Question

Hint for Lebesgue theory/functional analysis type of problem

Compact matrix integral operator bound via its kernel

Understanding this integral from a measure theory perspective.

Completeness of $l_1 ^\infty$

Property of functions: do there exist counterexamples?

Proving fact about shifts of $L^\infty$ functions

How to prove that a Schwartz function belongs to $L^p$?

If $0<\mu(X)<\infty$ and $0<p<q< \infty$. Is $(\int_X |f|^p) ^\frac{1}{p}\leq \int_X |f|^q d\mu) ^\frac{1}{q}$ true?

$L^p$ convergence of infinitesimal generator

function $f\notin L^{\infty}(\Omega)$, but $f\in L^p(\Omega)$ for all $1\le p <\infty$

Does $L^p$ have a basis for which the Pythagorean identity with exponent $p$ holds?

exercise: dual of an Lp-space

Convolution with imaginary Gaussian cannot be a $(p, p)$ operator unless $p=2$

Uniform Convergence Implies $L^2$ Convergence and $L^2$ Convergence Implies $L^1$ Convergence

Normalize a function and a measure so that the $L^p$ norm is $1$ for two values of $p$

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