Question

Convergence of a product of sequences convergent in mean when one of them is bounded

score 179 · Answer 1 · 2026-04-13 00:03:28

179

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Convergence of a product of sequences convergent in mean when one of them is bounded

Published on 13 Apr 2026 - 0:03

score 75 · Answer 2 · 2015-03-24 17:06:49

75

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Find all functions such that $ (\int _0 ^1 xf(x) dx)^3 = \frac{4}{25} \int _0 ^1 f(x)^3 dx$

Published on 24 Mar 2015 - 17:06

score 731 · Answer 3 · 2015-03-24 22:22:42

731

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$\|fg\|_{L^2(\Omega)}\leq \|f\|_{L^2(\Omega)}\|g\|_{L^\infty(\Omega)}$

Published on 24 Mar 2015 - 22:22

score 1.6k · Answer 4 · 2015-03-26 02:04:28

1.6k

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Prove that $T$ is bounded if $\langle Tx, y \rangle = \langle x, T^*y \rangle$

Published on 26 Mar 2015 - 2:04

score 363 · Answer 5 · 2015-03-26 14:56:34

363

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show $\ell^p$ is dense in $\ell^q$

Published on 26 Mar 2015 - 14:56

score 103 · Answer 6 · 2026-03-28 01:48:48

103

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Existence of extension of isometries on subspaces of $\ell_{p}(\mathbb N)$.

Published on 28 Mar 2026 - 1:48

score 232 · Answer 7 · 2026-04-09 06:12:07

232

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$\||f|^{2}f\|_{H^{s}}\leq C \|f\|^{2}_{L^{\infty}} \|f\|_{H^{s}}$ for $s>0, f\in H^{s}(\mathbb R)$?

Published on 09 Apr 2026 - 6:12

score 17 · Answer 8 · 2026-04-13 00:09:08

17

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Does $\partial_b u(\cdot,b) \in L^2(A)$ for fixed $b$ imply that $u(\cdot,b) \in L^2(A)$?

Published on 13 Apr 2026 - 0:09

score 554 · Answer 9 · 2026-04-13 06:18:25

554

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Projection on closed subspace of $L^p$, $1<p<\infty$

Published on 13 Apr 2026 - 6:18

score 89 · Answer 10 · 2015-04-02 00:04:26

89

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If $f \in \mathcal{L}^{2}(\mathbb{R}^{n})$, does it imply that it is bounded almost everywhere?

Published on 02 Apr 2015 - 0:04

score 191 · Answer 11 · 2026-04-12 13:38:43

191

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Characterization of $L^p$ function for $p>1$

Published on 12 Apr 2026 - 13:38

score 998 · Answer 12 · 2015-04-03 06:22:36

998

Views

Show that a subspace is proper dense in $l^1$ sequence space. L^1 space.

Published on 03 Apr 2015 - 6:22

score 337 · Answer 13 · 2015-04-03 19:14:57

337

Views

Dense subset of $L^p[a,b]$

Published on 03 Apr 2015 - 19:14

score 1.4k · Answer 14 · 2026-04-11 12:56:24

1.4k

Views

Showing that $L^2\subset L^1$ for $L^2([0,t_f])$, with $t_f$ a fixed positive number.

Published on 11 Apr 2026 - 12:56

score 1.1k · Answer 15 · 2026-04-12 09:39:47

1.1k

Views

Definition of Strong Convergence in $L^p$

Published on 12 Apr 2026 - 9:39

List Question

Convergence of a product of sequences convergent in mean when one of them is bounded

Find all functions such that $ (\int _0 ^1 xf(x) dx)^3 = \frac{4}{25} \int _0 ^1 f(x)^3 dx$

$\|fg\|_{L^2(\Omega)}\leq \|f\|_{L^2(\Omega)}\|g\|_{L^\infty(\Omega)}$

Prove that $T$ is bounded if $\langle Tx, y \rangle = \langle x, T^*y \rangle$

show $\ell^p$ is dense in $\ell^q$

Existence of extension of isometries on subspaces of $\ell_{p}(\mathbb N)$.

$\||f|^{2}f\|_{H^{s}}\leq C \|f\|^{2}_{L^{\infty}} \|f\|_{H^{s}}$ for $s>0, f\in H^{s}(\mathbb R)$?

Does $\partial_b u(\cdot,b) \in L^2(A)$ for fixed $b$ imply that $u(\cdot,b) \in L^2(A)$?

Projection on closed subspace of $L^p$, $1<p<\infty$

If $f \in \mathcal{L}^{2}(\mathbb{R}^{n})$, does it imply that it is bounded almost everywhere?

Characterization of $L^p$ function for $p>1$

Show that a subspace is proper dense in $l^1$ sequence space. L^1 space.

Dense subset of $L^p[a,b]$

Showing that $L^2\subset L^1$ for $L^2([0,t_f])$, with $t_f$ a fixed positive number.

Definition of Strong Convergence in $L^p$

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