List questions from lp-spaces

Published on 22 Jan 2015 - 4:20

362

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$f\in L^1\cap L^2$ implies $\hat f \in L^1$?

Published on 22 Jan 2015 - 16:09

97

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Showing a function is in $L^1(\mathbb{R})$

Published on 22 Jan 2015 - 23:09

813

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Test functions are dense in $L^p$?

Published on 23 Jan 2015 - 17:26

187

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A question about weak convergence in Lp space

Published on 09 Apr 2026 - 3:39

73

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$f\in L^p(X,\mu)$ , $f-1\in L^q(X,\mu)$ then $\mu(X) < \infty $

Published on 26 Jan 2015 - 19:59

75

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Show that $ \int_I x^{-\frac{1}{4}} $sin$ x \;dx \leq \pi^{\frac{3}{4}}$.

Published on 27 Jan 2015 - 20:12

579

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Proving a subset of $l_2$ is closed

Published on 12 Apr 2026 - 18:54

71

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Is it possible to have simultaneously $\int_I(f(x)-\text{sin} x)^2 dx\leq \frac{4}{9}$ and $\int_I(f(x)-\text{cos} x)^2 dx\leq \frac{1}{9}$?

Published on 28 Jan 2015 - 22:55

93

Views

Show that $f=0$ a.e. if $|\int_I f|^p \leq c|I|^{p-1}\int_I |f|^p$ with $0<c<1$

Published on 29 Jan 2015 - 0:58

91

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Unit balls and the Schatten norms

Published on 01 Apr 2026 - 8:55

67

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$\ell_q$ is not finitely representable in $\ell_p$ if $2<q<p$.

Published on 09 Apr 2026 - 7:19

241

Views

Weak convergence - $f_n$ "goes up the spout"

Published on 29 Jan 2015 - 18:41

84

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Compute $\lim_{|h|\rightarrow \infty} \int_{\mathbb{R}^n} |f(y+h)+f(y)|^p dy$

Published on 12 Apr 2026 - 6:16

1.1k

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Dense subset in sequence space

Published on 12 Apr 2026 - 13:58

List Question

Limit of products in $L^p(\mathbb R^d)$

$f\in L^1\cap L^2$ implies $\hat f \in L^1$?

Showing a function is in $L^1(\mathbb{R})$

Test functions are dense in $L^p$?

A question about weak convergence in Lp space

$f\in L^p(X,\mu)$ , $f-1\in L^q(X,\mu)$ then $\mu(X) < \infty $

Show that $ \int_I x^{-\frac{1}{4}} $sin$ x \;dx \leq \pi^{\frac{3}{4}}$.

Proving a subset of $l_2$ is closed

Is it possible to have simultaneously $\int_I(f(x)-\text{sin} x)^2 dx\leq \frac{4}{9}$ and $\int_I(f(x)-\text{cos} x)^2 dx\leq \frac{1}{9}$?

Show that $f=0$ a.e. if $|\int_I f|^p \leq c|I|^{p-1}\int_I |f|^p$ with $0<c<1$

Unit balls and the Schatten norms

$\ell_q$ is not finitely representable in $\ell_p$ if $2<q<p$.

Weak convergence - $f_n$ "goes up the spout"

Compute $\lim_{|h|\rightarrow \infty} \int_{\mathbb{R}^n} |f(y+h)+f(y)|^p dy$

Dense subset in sequence space

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