List questions from lp-spaces

Published on 02 Aug 2019 - 21:03

42

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Integral equation exercise

Published on 25 Mar 2026 - 11:08

103

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How can we compute the Fréchet derivative of $q\mapsto\int\frac{(pf)^2}q\:{\rm d}\lambda$?

Published on 25 Mar 2026 - 15:28

200

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Minimize $q\mapsto\int\frac{(pf)^2}q\:{\rm d}\lambda$ subject to $\int q\:{\rm }\lambda=1$ using the method of Lagrange multipliers

Published on 27 Mar 2026 - 0:58

86

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The unit sphere with the $L^2$ norm in $H_0^1(\Omega)$ is weakly closed in $H_0^1(\Omega)$.

Published on 25 Mar 2026 - 14:36

220

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Pointwise convergence of Fourier-Legendre Series expansion

Published on 25 Mar 2026 - 8:12

181

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Show $\int\frac{f(u+\varepsilon v)-f(u)}\varepsilon\:{\rm d}\mu\xrightarrow{\varepsilon\to0}\int f'(u)v\:{\rm d}\mu$ for a large class of $f,u,v$

Published on 25 Mar 2026 - 15:12

71

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$L^p$ inequalities

Published on 05 Aug 2019 - 19:40

298

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Is the sequence space $\ell^p$ closed under the Cauchy product?

Published on 23 Feb 2026 - 2:09

45

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Do these integral orthogonality relations imply pointwise relations?

Published on 27 Mar 2026 - 3:49

32

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A motivational question regarding compact topological groups.

Published on 26 Mar 2026 - 6:33

80

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Bounddeness in $L^p$ norm implies boundedness in infinity norm

Published on 09 Aug 2019 - 5:07

688

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Sum of functions in Lp spaces for $p<1$

Published on 10 Aug 2019 - 12:48

96

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Interpolation type theorem for multiplication operator on measure space. Is it trivial?

Published on 25 Mar 2026 - 3:01

80

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A kind of Lebesgue differentiation theorem for general sets

Published on 30 Mar 2026 - 15:14

List Question

(Componentwise) Convergent sequences in $l_p$ spaces

Integral equation exercise

How can we compute the Fréchet derivative of $q\mapsto\int\frac{(pf)^2}q\:{\rm d}\lambda$?

Minimize $q\mapsto\int\frac{(pf)^2}q\:{\rm d}\lambda$ subject to $\int q\:{\rm }\lambda=1$ using the method of Lagrange multipliers

The unit sphere with the $L^2$ norm in $H_0^1(\Omega)$ is weakly closed in $H_0^1(\Omega)$.

Pointwise convergence of Fourier-Legendre Series expansion

Show $\int\frac{f(u+\varepsilon v)-f(u)}\varepsilon\:{\rm d}\mu\xrightarrow{\varepsilon\to0}\int f'(u)v\:{\rm d}\mu$ for a large class of $f,u,v$

$L^p$ inequalities

Is the sequence space $\ell^p$ closed under the Cauchy product?

Do these integral orthogonality relations imply pointwise relations?

A motivational question regarding compact topological groups.

Bounddeness in $L^p$ norm implies boundedness in infinity norm

Sum of functions in Lp spaces for $p<1$

Interpolation type theorem for multiplication operator on measure space. Is it trivial?

A kind of Lebesgue differentiation theorem for general sets

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