List questions from lp-spaces

Published on 25 Mar 2026 - 23:37

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a condition given by step functions implies the condition holds for L^q space

Published on 16 Jun 2014 - 1:28

927

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$L^p$ norm of a measurable function is bounded by its operation on step functions

Published on 17 Jun 2014 - 7:14

390

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Hardy Littlewood maximal function and integral comparison.

Published on 19 Jun 2014 - 15:57

1.1k

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Convergence in $L^p$ plus bounded gradient implies that the limit belongs to $W^{1,p}$?

Published on 31 Mar 2026 - 19:16

156

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Example of open operator but not closed

Published on 31 Mar 2026 - 8:43

1.7k

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Show that $\lim _{r \to 0} \|T_rf−f\|_{L_p} =0.$

Published on 01 Apr 2026 - 3:44

2.6k

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Why are $L^p$-spaces so ubiquitous?

Published on 31 Mar 2026 - 19:13

202

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Equivalent Definitions of the $L_2$ inner product.

Published on 23 Jun 2014 - 2:12

63

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Unique extension of operators

Published on 23 Jun 2014 - 6:43

63

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$L_p$ spaces and tail estimates

Published on 24 Jun 2014 - 10:16

532

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Increasing sequence of closed subspaces of $L^2$

Published on 28 Mar 2026 - 3:34

269

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Are bounded linear functionals on $L^{\infty}$ of “bounded variation?”

Published on 25 Jun 2014 - 1:13

70

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If $u_n \rightharpoonup u$ in $L^2(\Omega)$, does $u_n^+ \rightharpoonup u^+$ in $L^2(\Omega)$?

Published on 25 Jun 2014 - 14:02

99

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Find a sequence of r.v's satisfying the following conditions

Published on 25 Mar 2026 - 23:39

List Question

negative Sobolev space contains $L^1$ for a compact domain

a condition given by step functions implies the condition holds for L^q space

$L^p$ norm of a measurable function is bounded by its operation on step functions

Hardy Littlewood maximal function and integral comparison.

Convergence in $L^p$ plus bounded gradient implies that the limit belongs to $W^{1,p}$?

Example of open operator but not closed

Show that $\lim _{r \to 0} \|T_rf−f\|_{L_p} =0.$

Why are $L^p$-spaces so ubiquitous?

Equivalent Definitions of the $L_2$ inner product.

Unique extension of operators

$L_p$ spaces and tail estimates

Increasing sequence of closed subspaces of $L^2$

Are bounded linear functionals on $L^{\infty}$ of “bounded variation?”

If $u_n \rightharpoonup u$ in $L^2(\Omega)$, does $u_n^+ \rightharpoonup u^+$ in $L^2(\Omega)$?

Find a sequence of r.v's satisfying the following conditions

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