Question

Hardy's Inequality: Problems $3.14$ and $3.15$ in Rudin's RCA

score 1k · Answer 1 · 2026-04-16 06:30:09

1k

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Hardy's Inequality: Problems $3.14$ and $3.15$ in Rudin's RCA

Published on 16 Apr 2026 - 6:30

score 159 · Answer 2 · 2026-04-17 10:00:05

159

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Show that $\lim_{t \to \infty} t^p μ({x ∈ X : |f(x)| >t})=0$.

Published on 17 Apr 2026 - 10:00

score 314 · Answer 3 · 2026-04-14 21:14:34

314

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A certain converse of Hölder's inequality for $L^\infty$ space.

Published on 14 Apr 2026 - 21:14

score 110 · Answer 4 · 2026-04-17 00:13:43

110

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$\{(1/\sqrt\pi) (1-\sqrt{-1}x)^n/(1＋\sqrt{-1}x)^{n＋1}$ $(n=0,\pm1,\pm2,\ldots)\}⊂L^2(-∞,∞)$ is complete normalized orthogonal basis

Published on 17 Apr 2026 - 0:13

score 64 · Answer 5 · 2026-04-16 01:34:10

64

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$L^1$ space is proper subset of interval on $L^1$ space?

Published on 16 Apr 2026 - 1:34

score 388 · Answer 6 · 2026-04-16 07:40:07

388

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Can $L^p(\mathbb{R})$ and $L^p[0,1]$ be isomorphic?

Published on 16 Apr 2026 - 7:40

score 97 · Answer 7 · 2026-04-09 05:10:32

97

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Are ℓp spaces discrete spaces?

Published on 09 Apr 2026 - 5:10

score 86 · Answer 8 · 2026-04-17 15:08:05

86

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$f+g\in L^p$ if $f,g \in L^p$

Published on 17 Apr 2026 - 15:08

score 80 · Answer 9 · 2026-04-16 08:43:26

80

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Is $L^1(\mathbb R^n)\cap L^2_{loc}(\mathbb R^n)$ included in $L^2(\mathbb R^n)\,$?

Published on 16 Apr 2026 - 8:43

score 202 · Answer 10 · 2026-04-14 10:13:40

202

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Convergence of a series of functions in L^p

Published on 14 Apr 2026 - 10:13

score 37 · Answer 11 · 2026-04-13 19:24:38

37

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For which $p \in [1,+\infty)$ $f(x,y) \in L^p(\Omega)$

Published on 13 Apr 2026 - 19:24

score 191 · Answer 12 · 2026-04-15 09:46:31

191

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Do convergence in $L^2$ and boundedness of gradients in $L^2$ imply convergence in $W^{1,2}$?

Published on 15 Apr 2026 - 9:46

score 176 · Answer 13 · 2026-04-09 07:17:52

176

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How does Holder's inequality apply to the expectation operator when using the infinity norm?

Published on 09 Apr 2026 - 7:17

score 112 · Answer 14 · 2026-04-13 06:41:47

112

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What will be the spectral measure corresponding to $M_{\varphi}$ if $\varphi$ is real-valued $\mu$ a.e.?

Published on 13 Apr 2026 - 6:41

score 259 · Answer 15 · 2026-04-09 17:16:15

259

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Mistaken proof that every bounded linear operator on $L^2$ has an integral kernel

Published on 09 Apr 2026 - 17:16

List Question

Hardy's Inequality: Problems $3.14$ and $3.15$ in Rudin's RCA

Show that $\lim_{t \to \infty} t^p μ({x ∈ X : |f(x)| >t})=0$.

A certain converse of Hölder's inequality for $L^\infty$ space.

$\{(1/\sqrt\pi) (1-\sqrt{-1}x)^n/(1＋\sqrt{-1}x)^{n＋1}$ $(n=0,\pm1,\pm2,\ldots)\}⊂L^2(-∞,∞)$ is complete normalized orthogonal basis

$L^1$ space is proper subset of interval on $L^1$ space?

Can $L^p(\mathbb{R})$ and $L^p[0,1]$ be isomorphic?

Are ℓp spaces discrete spaces?

$f+g\in L^p$ if $f,g \in L^p$

Is $L^1(\mathbb R^n)\cap L^2_{loc}(\mathbb R^n)$ included in $L^2(\mathbb R^n)\,$?

Convergence of a series of functions in L^p

For which $p \in [1,+\infty)$ $f(x,y) \in L^p(\Omega)$

Do convergence in $L^2$ and boundedness of gradients in $L^2$ imply convergence in $W^{1,2}$?

How does Holder's inequality apply to the expectation operator when using the infinity norm?

What will be the spectral measure corresponding to $M_{\varphi}$ if $\varphi$ is real-valued $\mu$ a.e.?

Mistaken proof that every bounded linear operator on $L^2$ has an integral kernel

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