List questions from lp-spaces

Published on 14 Apr 2026 - 0:41

27

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Does convergence in $L^2$ imply smallness of $||f_n-f||_{L^2(\mathbb{R}^2\setminus B_R(0)}$ for large $R>0$ independent of $n$?

Published on 15 Apr 2026 - 9:47

67

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$\int_{\frac{\delta}{2}}^{\delta}\dfrac{F^{\prime}(x)}{F(\delta)}dx \leq C$

Published on 15 Apr 2026 - 21:07

74

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$\int_{I}|f(x)||g(x)|^{2}dx \leq \bigg(\int_{I}|f(x)|dx\bigg)\bigg(\int_{I}|g(x)|^{2}dx\bigg)^{\beta}$

Published on 17 Apr 2026 - 9:25

36

Views

Ratio of $\ell^p$ seminorms as dimension $n$ increases: $\frac{\|x^{(n)}\|_1}{\|x^{(n)}\|_q} \to \infty$ if $0< q < 1$ and $\|x^{(n)}\|_q \to \infty$?

Published on 16 Apr 2026 - 9:21

52

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$L_{p_n}$-norm $\to L_p$-norm for Random Variables

Published on 14 Apr 2026 - 14:50

123

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Parallelogram law in L1 space - Did not understand counter-example

Published on 15 May 2026 - 6:12

62

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Hamel basis of $\ell_p$ and $\ell_\infty$.

Published on 13 Apr 2026 - 16:17

53

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Does an isometric automorphism of $L_p := L_p (\Omega, \mu, X)$ preserve the support?

Published on 14 Apr 2026 - 12:50

58

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Does an isometric automorphism of $L_p (\mu, X)$ preserve pointwise convergence?

Published on 14 Apr 2026 - 7:31

36

Views

Finding a suitable mollifier $\phi$ so that $\lim_{k\to\infty}||f - h\ast\phi||_\infty=0$ for a continuous function $f$ vanishing at the infinity

Published on 13 Apr 2026 - 18:23

88

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exists $f\not\in L^1(X)$ such that $f\in L^p(X)$

Published on 16 Apr 2026 - 20:03

81

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$\forall f\in L^p : f\in L^1$

Published on 16 Apr 2026 - 2:50

36

Views

Intersection of infinitely many $L^p$ spaces over $\mathbb{R}$: reference-request

Published on 15 Apr 2026 - 7:41

91

Views

Reference request about the parabolic Sobolev spaces

Published on 14 Apr 2026 - 23:51

List Question

Compact embedding $L^p$ to $L^q$

Does convergence in $L^2$ imply smallness of $||f_n-f||_{L^2(\mathbb{R}^2\setminus B_R(0)}$ for large $R>0$ independent of $n$?

$\int_{\frac{\delta}{2}}^{\delta}\dfrac{F^{\prime}(x)}{F(\delta)}dx \leq C$

$\int_{I}|f(x)||g(x)|^{2}dx \leq \bigg(\int_{I}|f(x)|dx\bigg)\bigg(\int_{I}|g(x)|^{2}dx\bigg)^{\beta}$

Ratio of $\ell^p$ seminorms as dimension $n$ increases: $\frac{\|x^{(n)}\|_1}{\|x^{(n)}\|_q} \to \infty$ if $0< q < 1$ and $\|x^{(n)}\|_q \to \infty$?

$L_{p_n}$-norm $\to L_p$-norm for Random Variables

Parallelogram law in L1 space - Did not understand counter-example

Hamel basis of $\ell_p$ and $\ell_\infty$.

Does an isometric automorphism of $L_p := L_p (\Omega, \mu, X)$ preserve the support?

Does an isometric automorphism of $L_p (\mu, X)$ preserve pointwise convergence?

Finding a suitable mollifier $\phi$ so that $\lim_{k\to\infty}||f - h\ast\phi||_\infty=0$ for a continuous function $f$ vanishing at the infinity

exists $f\not\in L^1(X)$ such that $f\in L^p(X)$

$\forall f\in L^p : f\in L^1$

Intersection of infinitely many $L^p$ spaces over $\mathbb{R}$: reference-request

Reference request about the parabolic Sobolev spaces

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