Question

Weak $L^{p}$ spaces are quasi-normed?

score 1.9k · Answer 1 · 2026-03-25 19:03:18

1.9k

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Weak $L^{p}$ spaces are quasi-normed?

Published on 25 Mar 2026 - 19:03

score 247 · Answer 2 · 2026-03-25 19:01:06

247

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Upper Bound for Operator Norm in Marcinkiewicz Interpolation Theorem

Published on 25 Mar 2026 - 19:01

score 87 · Answer 3 · 2026-03-25 23:42:33

87

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Do we have $\lVert f\rVert_{L^p(X)}=\int_0^\infty p\alpha^{p-1}d_f(\alpha)\,\mathrm{d}\alpha$ for non $\sigma$-finite $X$?

Published on 25 Mar 2026 - 23:42

score 530 · Answer 4 · 2026-04-21 17:32:09

530

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Intuition regrading the weak $L^p$ functions

Published on 21 Apr 2026 - 17:32

score 524 · Answer 5 · 2026-03-25 19:05:41

524

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Intuition of the Lorentz norm in an Wikipedia article

Published on 25 Mar 2026 - 19:05

score 1.5k · Answer 6 · 2026-04-06 07:20:57

1.5k

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Normability of weak $L^p$-spaces

Published on 06 Apr 2026 - 7:20

score 112 · Answer 7 · 2026-03-25 22:11:02

112

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the additivity for space of weak $L^p$

Published on 25 Mar 2026 - 22:11

score 113 · Answer 8 · 2026-04-06 06:14:55

113

Views

some inequality for weal-$L^p$

Published on 06 Apr 2026 - 6:14

score 119 · Answer 9 · 2026-03-25 19:07:07

119

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Show that$\,\,\int_{|f|\leq s}|f\,|^{q}\,d\mu\leq\frac{q}{q-p}s^{q-p}\lVert f\,\rVert_{L^{p,\infty}}^p\,\,,$ where $0<p<q<\infty$

Published on 25 Mar 2026 - 19:07

score 226 · Answer 10 · 2026-03-25 23:42:41

226

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Show that $f$ is belongs to weak $L^{1}(E)$ and $f$ is bounded on $E$. Then $f$ is $L^{p}(E)$ for each $1<p<\infty$

Published on 25 Mar 2026 - 23:42

score 73 · Answer 11 · 2026-03-25 19:07:14

For $0<p<\infty.$Show that $\left\lVert\max_{1\leq j\leq m}|f_j|\right\rVert_{L^{p,\infty}}^{p}\leq\sum_{j=1}^{m}\lVert f_j\rVert_{L^{p,\infty}}^p$

score 134 · Answer 12 · 2026-03-25 19:07:14

134

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$\lVert f_{1}+\cdots+f_{m}\rVert_{L^{p,\infty}}^{p}\le \frac{2-p}{1-p}\sum_{j=1}^{m}\lVert f_{j}\rVert_{L^{p,\infty}}^{p}$

Published on 25 Mar 2026 - 19:07

score 165 · Answer 13 · 2026-04-06 07:35:56

165

Views

Convolution and weak $L^p$ spaces

Published on 06 Apr 2026 - 7:35

score 109 · Answer 14 · 2026-03-25 19:02:38

109

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Bounded gradient in weak $L^1$ implies compactness in $L^1$ (?) Relation to fractional Sobolev compactness.

Published on 25 Mar 2026 - 19:02

score 67 · Answer 15 · 2026-03-25 19:01:10

67

Views

Weak convergence in $L^{p,\infty}$

Published on 25 Mar 2026 - 19:01

List Question

Weak $L^{p}$ spaces are quasi-normed?

Upper Bound for Operator Norm in Marcinkiewicz Interpolation Theorem

Do we have $\lVert f\rVert_{L^p(X)}=\int_0^\infty p\alpha^{p-1}d_f(\alpha)\,\mathrm{d}\alpha$ for non $\sigma$-finite $X$?

Intuition regrading the weak $L^p$ functions

Intuition of the Lorentz norm in an Wikipedia article

Normability of weak $L^p$-spaces

the additivity for space of weak $L^p$

some inequality for weal-$L^p$

Show that$\,\,\int_{|f|\leq s}|f\,|^{q}\,d\mu\leq\frac{q}{q-p}s^{q-p}\lVert f\,\rVert_{L^{p,\infty}}^p\,\,,$ where $0<p<q<\infty$

Show that $f$ is belongs to weak $L^{1}(E)$ and $f$ is bounded on $E$. Then $f$ is $L^{p}(E)$ for each $1<p<\infty$

For $0<p<\infty.$Show that $\left\lVert\max_{1\leq j\leq m}|f_j|\right\rVert_{L^{p,\infty}}^{p}\leq\sum_{j=1}^{m}\lVert f_j\rVert_{L^{p,\infty}}^p$

$\lVert f_{1}+\cdots+f_{m}\rVert_{L^{p,\infty}}^{p}\le \frac{2-p}{1-p}\sum_{j=1}^{m}\lVert f_{j}\rVert_{L^{p,\infty}}^{p}$

Convolution and weak $L^p$ spaces

Bounded gradient in weak $L^1$ implies compactness in $L^1$ (?) Relation to fractional Sobolev compactness.

Weak convergence in $L^{p,\infty}$

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