List questions from lp-spaces

Published on 11 Apr 2026 - 8:21

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Convergence question about Lp norm when p tends to zero

Published on 09 Apr 2026 - 13:24

562

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$L^p$ subspaces of $L^1$

Published on 15 Apr 2026 - 20:35

528

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Proving the convergence of limit of the integral

Published on 14 Apr 2026 - 15:33

443

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Approximation by $C^\infty$-function

Published on 10 Apr 2026 - 22:57

1.7k

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$\|f\|_p\to \|f\|_\infty$ under general assumptions

Published on 16 Apr 2026 - 8:22

727

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$\lim_{n\to\infty}\|f-f_n\|_p=0\implies \lim_{n\to\infty}\|f_n\|_p=\|f\|_p$

Published on 17 Apr 2026 - 11:05

358

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Use Holder inequality to show $f_n * g_n$ converges to $f*g$ uniformly

Published on 16 Apr 2026 - 4:45

1.8k

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Convergence in $L^1$ and uniformly bounded in $L^2$ implies limit is in $L^2$

Published on 15 Apr 2026 - 23:46

504

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Prove that $L^{\infty}(\mathbb R)\cap C(\mathbb R)$ is not dense in $L^{\infty}(\mathbb R)$

Published on 13 Apr 2026 - 23:19

1.6k

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The dual of $L^\infty$ for Borel measures and $L^\infty$ functions vanishing at infinity

Published on 13 Apr 2026 - 19:04

302

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If $f_{n}\to f$ a.e on $[0,1]$ and $f_{n}, f \in L^{p}[0,1]$ , then for all $g \in L^{q}[0,1]$ show that $\int f_{n}.g \to \int f.g$

Published on 17 Apr 2026 - 1:54

34

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Fourier transformation on $L^2(G)$.

Published on 13 Apr 2026 - 14:00

481

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Convergence in $L_1$ and uniformly bounded in $L^2$ implies convergence in $L^p$, $1<p<2$.

Published on 16 Apr 2026 - 12:28

1k

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$f\in L^{p}$ iff $\sum_{n=1}^{\infty} 2^{np}(\mu(\{\ x : |f(x)| > 2^{n} \}\ )) < \infty$

Published on 16 Apr 2026 - 6:55

List Question

When weighted $L^2-$norm are comparable?

Convergence question about Lp norm when p tends to zero

$L^p$ subspaces of $L^1$

Proving the convergence of limit of the integral

Approximation by $C^\infty$-function

$\|f\|_p\to \|f\|_\infty$ under general assumptions

$\lim_{n\to\infty}\|f-f_n\|_p=0\implies \lim_{n\to\infty}\|f_n\|_p=\|f\|_p$

Use Holder inequality to show $f_n * g_n$ converges to $f*g$ uniformly

Convergence in $L^1$ and uniformly bounded in $L^2$ implies limit is in $L^2$

Prove that $L^{\infty}(\mathbb R)\cap C(\mathbb R)$ is not dense in $L^{\infty}(\mathbb R)$

The dual of $L^\infty$ for Borel measures and $L^\infty$ functions vanishing at infinity

If $f_{n}\to f$ a.e on $[0,1]$ and $f_{n}, f \in L^{p}[0,1]$ , then for all $g \in L^{q}[0,1]$ show that $\int f_{n}.g \to \int f.g$

Fourier transformation on $L^2(G)$.

Convergence in $L_1$ and uniformly bounded in $L^2$ implies convergence in $L^p$, $1<p<2$.

$f\in L^{p}$ iff $\sum_{n=1}^{\infty} 2^{np}(\mu(\{\ x : |f(x)| > 2^{n} \}\ )) < \infty$

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