List questions from lp-spaces

Published on 10 Apr 2026 - 14:34

82

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Prove that $\|f\|_{p,q}= \inf\{\|g\|_p+\|h\|_q;f=g+h, g \in L^p(R), h \in L^q(R)\}$ is a norm on $L^p(R)+L^q(R) $

Published on 10 May 2026 - 12:39

77

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Show that $N(f)= \inf\{\|g\|_p+\|h\|_q;f=g+h, g \in L^p(\mathbb{R}), h \in L^q(\mathbb{R})\}$ is a norm on $L^p(\mathbb{R})+L^q(\mathbb{R}) $

Published on 10 May 2026 - 13:51

213

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Maximum ratio of L^p norms

Published on 15 Apr 2026 - 10:43

194

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Convolution identically $0$ implies $f =0$?

Published on 10 Apr 2026 - 4:18

1.4k

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Behavior of infinite convolution products

Published on 13 Apr 2026 - 18:14

87

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The openness of positive sequences in $\ell^{2}$

Published on 12 Apr 2026 - 21:12

116

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$\sup_{\|\,f\|_{L^2(\mu)}=1}\big(\int_X \varphi_1^2\, f^2\,d\mu + \int_X \varphi_2^2 \,f^2\,d\mu\big)=\big\|\varphi_1^2+\varphi_2^2\big\|_\infty$

Published on 17 Apr 2026 - 4:49

179

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Does $X^p_n \longrightarrow X^p$ in $L^1$ imply $X_n \longrightarrow X$ in $L^p$?

Published on 16 Apr 2026 - 2:11

49

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New norms on $L^2$

Published on 14 Apr 2026 - 17:57

70

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Maximal growth condition for embedding of Orlicz spaces

Published on 03 May 2026 - 17:52

465

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Linear map between $L^p$ and $L^q$.

Published on 14 Apr 2026 - 5:00

1.7k

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Intuition behind Lebesgue spaces: Lp, L^p, $\mathcal L^p$ or $L^p$ / $\ell^p$?

Published on 16 Apr 2026 - 13:17

626

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Closed and bounded but not compact subset of $\ell^1$

Published on 13 Apr 2026 - 14:55

85

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How to prove $\|P|X|^\theta\|_{p/\theta} \le \|P|X|\|_p^{\theta}$

Published on 29 Apr 2026 - 12:30

List Question

About a Sobolev function that admits a Lipschitz representative

Prove that $\|f\|_{p,q}= \inf\{\|g\|_p+\|h\|_q;f=g+h, g \in L^p(R), h \in L^q(R)\}$ is a norm on $L^p(R)+L^q(R) $

Show that $N(f)= \inf\{\|g\|_p+\|h\|_q;f=g+h, g \in L^p(\mathbb{R}), h \in L^q(\mathbb{R})\}$ is a norm on $L^p(\mathbb{R})+L^q(\mathbb{R}) $

Maximum ratio of L^p norms

Convolution identically $0$ implies $f =0$?

Behavior of infinite convolution products

The openness of positive sequences in $\ell^{2}$

$\sup_{\|\,f\|_{L^2(\mu)}=1}\big(\int_X \varphi_1^2\, f^2\,d\mu + \int_X \varphi_2^2 \,f^2\,d\mu\big)=\big\|\varphi_1^2+\varphi_2^2\big\|_\infty$

Does $X^p_n \longrightarrow X^p$ in $L^1$ imply $X_n \longrightarrow X$ in $L^p$?

New norms on $L^2$

Maximal growth condition for embedding of Orlicz spaces

Linear map between $L^p$ and $L^q$.

Intuition behind Lebesgue spaces: Lp, L^p, $\mathcal L^p$ or $L^p$ / $\ell^p$?

Closed and bounded but not compact subset of $\ell^1$

How to prove $\|P|X|^\theta\|_{p/\theta} \le \|P|X|\|_p^{\theta}$

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