List questions from lp-spaces

Published on 09 Apr 2026 - 16:05

138

Views

Find $f$ such that $\|f\|_p=1$ for every $p\geq 1$.

Published on 16 Apr 2026 - 1:14

33

Views

Showing that every $L^p(\mathbb{R}^n)$ function also belongs to the weak $L^p(\mathbb{R}^n)$

Published on 15 Apr 2026 - 11:19

138

Views

Showing that $q(f) \leq ||f||$ for weak $L^p(\mathbb{R}^n)$ norm $||.||$ and quasi-norm $q(.)$ with $f$ belonging to weak $L^p(\mathbb{R}^n)$

Published on 15 Apr 2026 - 17:46

63

Views

$L^1$ convergence and continuous functions/transformaton

Published on 12 Apr 2026 - 5:42

23

Views

Proving $f_\alpha(x) = x^{-a} \in L^p((0,1))$ for $a > 0, ap < 1$

Published on 16 Apr 2026 - 8:47

57

Views

No closed set in $\ell^2$

Published on 12 Apr 2026 - 23:02

196

Views

Convergence almost uniformly implies convergence in $L_\infty$

Published on 17 Apr 2026 - 9:41

93

Views

Product of two sequences that converge weakly

Published on 13 Apr 2026 - 18:06

51

Views

Show that $f_n \rightarrow f$ in $L_{\infty}$ if and only if $\{f_n\} \rightarrow f$ uniformly

Published on 15 Apr 2026 - 20:50

65

Views

What happen with $p=\infty$ interpolation spaces

Published on 14 Apr 2026 - 1:35

111

Views

Measurability of $L^2$-valued random function

Published on 15 Apr 2026 - 13:12

260

Views

Bergman Space is a Hilbert Space Conway book

Published on 11 Apr 2026 - 23:29

168

Views

Prove that this subset of $l^{2}$ is open

Published on 14 Apr 2026 - 16:28

269

Views

Upper bound of Khintchine inequality

Published on 13 Apr 2026 - 1:12

List Question

Poincare Inequality for Mean-Zero Functions

Find $f$ such that $\|f\|_p=1$ for every $p\geq 1$.

Showing that every $L^p(\mathbb{R}^n)$ function also belongs to the weak $L^p(\mathbb{R}^n)$

Showing that $q(f) \leq ||f||$ for weak $L^p(\mathbb{R}^n)$ norm $||.||$ and quasi-norm $q(.)$ with $f$ belonging to weak $L^p(\mathbb{R}^n)$

$L^1$ convergence and continuous functions/transformaton

Proving $f_\alpha(x) = x^{-a} \in L^p((0,1))$ for $a > 0, ap < 1$

No closed set in $\ell^2$

Convergence almost uniformly implies convergence in $L_\infty$

Product of two sequences that converge weakly

Show that $f_n \rightarrow f$ in $L_{\infty}$ if and only if $\{f_n\} \rightarrow f$ uniformly

What happen with $p=\infty$ interpolation spaces

Measurability of $L^2$-valued random function

Bergman Space is a Hilbert Space Conway book

Prove that this subset of $l^{2}$ is open

Upper bound of Khintchine inequality

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