List questions from lp-spaces

Published on 13 Apr 2026 - 1:12

46

Views

$\|\chi_A*\chi_B\|_{\mathbb L^\infty}\leq \min\{\lambda(A),\lambda(B)\}$

Published on 14 Apr 2026 - 8:06

46

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$f_n\rightarrow f$ in every $L^p(\mathbb R^d)$

Published on 16 Apr 2026 - 20:04

41

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Average of translates converges to $0$ in $L^p$

Published on 12 Apr 2026 - 8:45

52

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Bounded surjective linear map from $L^p$ to $L^r$ with $r < p$

Published on 15 Apr 2026 - 0:32

50

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Do functions of Bounded Variation form a dense set?

Published on 13 Apr 2026 - 18:56

88

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Convergence in Integral and Bounded in Lp Implies Convergence in Measure?

Published on 28 Apr 2026 - 19:48

82

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Does uniform convergence in $L_p$ implies uniform convergence in probability?

Published on 14 May 2026 - 15:18

143

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$I-T : L^p(\mathbb R) \rightarrow L^p(\mathbb R)$ is not surjective

Published on 13 Apr 2026 - 22:05

600

Views

Estimate involving $L^{\infty}$ norm of function in $H^2(\mathbb{R}) \cap H^{-1/2}(\mathbb{R})$

Published on 15 May 2026 - 7:37

38

Views

How to show function raised to $-\alpha$ is in $L^p(\mathbb{R}^d)$ when $p\alpha < d$?

Published on 15 Apr 2026 - 8:05

166

Views

$L^p$ space inclusion when $\Omega$ does not contain sets of arbitrarily small measure

Published on 14 Apr 2026 - 17:33

268

Views

Bound on L2-Norm of Probability Distributions?

Published on 11 May 2026 - 3:46

52

Views

Which Lebesgue space is the domain of covariance?

Published on 12 Apr 2026 - 10:42

39

Views

Convergence in $L^p$ when $f_n \rightrightarrows 0$ given $\|f_n\|_2 = 1$

Published on 16 Apr 2026 - 11:17

List Question

Prove that certain integral operator on $L^1[0,\infty)$ is compact

$\|\chi_A*\chi_B\|_{\mathbb L^\infty}\leq \min\{\lambda(A),\lambda(B)\}$

$f_n\rightarrow f$ in every $L^p(\mathbb R^d)$

Average of translates converges to $0$ in $L^p$

Bounded surjective linear map from $L^p$ to $L^r$ with $r < p$

Do functions of Bounded Variation form a dense set?

Convergence in Integral and Bounded in Lp Implies Convergence in Measure?

Does uniform convergence in $L_p$ implies uniform convergence in probability?

$I-T : L^p(\mathbb R) \rightarrow L^p(\mathbb R)$ is not surjective

Estimate involving $L^{\infty}$ norm of function in $H^2(\mathbb{R}) \cap H^{-1/2}(\mathbb{R})$

How to show function raised to $-\alpha$ is in $L^p(\mathbb{R}^d)$ when $p\alpha < d$?

$L^p$ space inclusion when $\Omega$ does not contain sets of arbitrarily small measure

Bound on L2-Norm of Probability Distributions?

Which Lebesgue space is the domain of covariance?

Convergence in $L^p$ when $f_n \rightrightarrows 0$ given $\|f_n\|_2 = 1$

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