Question

$fg \in L^1$ for every $f \in L^2$ implies $g \in L^2$

score 132 · Answer 1 · 2024-03-06 23:35:20

132

Views

$fg \in L^1$ for every $f \in L^2$ implies $g \in L^2$

Published on 06 Mar 2024 - 23:35

score 29 · Answer 2 · 2024-03-11 06:45:30

29

Views

Amenable countable groups specifically for complex-valued functions in $l^\infty(G)$

Published on 11 Mar 2024 - 6:45

score 24 · Answer 3 · 2024-03-13 02:31:42

24

Views

For $1 \leq p<q<\infty$ if $X$ contains sets of arb small positive measure, then $L^p \not\subset L^q$.

Published on 13 Mar 2024 - 2:31

score 36 · Answer 4 · 2026-04-04 16:15:10

36

Views

Approximating a weakly convergent sequence "uniformly" by a dense subspace

Published on 04 Apr 2026 - 16:15

score 39 · Answer 5 · 2024-03-14 18:21:34

39

Views

Does the weak limit of a sequence in $L^2([0,1])$ vanish on the limit set of vanishing sets?

Published on 14 Mar 2024 - 18:21

score 35 · Answer 6 · 2024-03-14 18:28:43

35

Views

With finite $\mu$, suppose $f_n$ converges in measure to $f$, and for all $n$, $||f_n||_2\leq 1$. Prove $||f_n-f||_1\rightarrow 0$

Published on 14 Mar 2024 - 18:28

score 96 · Answer 7 · 2026-04-12 06:09:23

96

Views

$L^p$-estimates for one dimensional wave-equation with lower order pertubation

Published on 12 Apr 2026 - 6:09

score 34 · Answer 8 · 2026-04-11 13:34:04

34

Views

Some intersection of Schatten spaces gives a weak Schatten space?

Published on 11 Apr 2026 - 13:34

score 35 · Answer 9 · 2026-04-09 14:15:50

35

Views

convergence of functions.

Published on 09 Apr 2026 - 14:15

score 21 · Answer 10 · 2024-03-20 18:24:00

21

Views

Sequence of sequences $\{a^{(n)}\}_n \subseteq \ell^2$ with bounded members $|a^{(n)}_k| \leq 1$ has converging subseq.

Published on 20 Mar 2024 - 18:24

score 73 · Answer 11 · 2024-03-22 01:46:29

73

Views

Showing $\chi_A \ast \chi_B(x)$ is continuous if $m(A),m(B) \in (0,\infty)$.

Published on 22 Mar 2024 - 1:46

score 111 · Answer 12 · 2026-04-12 07:25:37

111

Views

Square integrable for universal approximation

Published on 12 Apr 2026 - 7:25

score 105 · Answer 13 · 2026-03-26 06:20:35

105

Views

The dual $(L^\infty)^{*}$ is not $L^1$ by constructing example

Published on 26 Mar 2026 - 6:20

score 32 · Answer 14 · 2026-03-28 16:20:42

32

Views

Prove operator $(Tf)(x)=sin(x)\cdot f(x)$ is not compact

Published on 28 Mar 2026 - 16:20

score 49 · Answer 15 · 2026-03-25 22:02:49

49

Views

Using Hahn Banach for switching between $L^p$ spaces

Published on 25 Mar 2026 - 22:02

List Question

$fg \in L^1$ for every $f \in L^2$ implies $g \in L^2$

Amenable countable groups specifically for complex-valued functions in $l^\infty(G)$

For $1 \leq p<q<\infty$ if $X$ contains sets of arb small positive measure, then $L^p \not\subset L^q$.

Approximating a weakly convergent sequence "uniformly" by a dense subspace

Does the weak limit of a sequence in $L^2([0,1])$ vanish on the limit set of vanishing sets?

With finite $\mu$, suppose $f_n$ converges in measure to $f$, and for all $n$, $||f_n||_2\leq 1$. Prove $||f_n-f||_1\rightarrow 0$

$L^p$-estimates for one dimensional wave-equation with lower order pertubation

Some intersection of Schatten spaces gives a weak Schatten space?

convergence of functions.

Sequence of sequences $\{a^{(n)}\}_n \subseteq \ell^2$ with bounded members $|a^{(n)}_k| \leq 1$ has converging subseq.

Showing $\chi_A \ast \chi_B(x)$ is continuous if $m(A),m(B) \in (0,\infty)$.

Square integrable for universal approximation

The dual $(L^\infty)^{*}$ is not $L^1$ by constructing example

Prove operator $(Tf)(x)=sin(x)\cdot f(x)$ is not compact

Using Hahn Banach for switching between $L^p$ spaces

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