Question

Twice continuously differentiable function $f:\Bbb R^2\to \Bbb R$ such that $f, f_{xx}, f_{yy}\in L^2$ is bounded

score 221 · Answer 1 · 2020-07-01 19:47:40

221

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Twice continuously differentiable function $f:\Bbb R^2\to \Bbb R$ such that $f, f_{xx}, f_{yy}\in L^2$ is bounded

Published on 01 Jul 2020 - 19:47

score 107 · Answer 2 · 2026-03-25 12:53:58

107

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$L^2$ norm of inverse differential operator

Published on 25 Mar 2026 - 12:53

score 589 · Answer 3 · 2020-07-02 08:20:12

589

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If $X_n$ converges to $X$ in $L_p$ and $Y_n$ converges to $Y$ in $L_p$ then $X_n + Y_n $ converges to $X + Y$ in $L_p$

Published on 02 Jul 2020 - 8:20

score 361 · Answer 4 · 2020-07-02 10:12:50

361

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Orthonormal basis in $L^2(\mathbb R)$

Published on 02 Jul 2020 - 10:12

score 311 · Answer 5 · 2026-03-29 10:07:44

311

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About essential range and essential supremum

Published on 29 Mar 2026 - 10:07

score 173 · Answer 6 · 2026-02-23 09:03:42

173

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Prove the relative compactness of a sequence in $L^p$

Published on 23 Feb 2026 - 9:03

score 241 · Answer 7 · 2026-03-27 02:39:49

241

Views

Weak Bernstein inequality for trigonometric polynomials

Published on 27 Mar 2026 - 2:39

score 91 · Answer 8 · 2026-04-04 02:37:40

91

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Fundamental set in the space of bounded sequences

Published on 04 Apr 2026 - 2:37

score 331 · Answer 9 · 2020-07-05 16:14:48

331

Views

How to prove $L_{2} ([0,1])$ $\cong$ $L_{2}(\mathbb{R})$

Published on 05 Jul 2020 - 16:14

score 45 · Answer 10 · 2026-03-27 11:48:55

45

Views

can sequences in $\ell^p$ with $0<p<1$ be multiplied by $n^\alpha$ and still fall in $\ell^1$?

Published on 27 Mar 2026 - 11:48

score 57 · Answer 11 · 2026-04-02 06:40:22

57

Views

$L^\infty(\mathbb{R}^n)$ function that is also homogenous with degree zero

Published on 02 Apr 2026 - 6:40

score 77 · Answer 12 · 2020-07-07 00:42:23

77

Views

Understanding proof of Jensen's inequality in Lieb-Loss

Published on 07 Jul 2020 - 0:42

score 589 · Answer 13 · 2026-03-26 04:31:17

589

Views

Show $l^p$ is not complete with the $q$ norm

Published on 26 Mar 2026 - 4:31

score 186 · Answer 14 · 2020-07-08 09:10:04

186

Views

multiplication of measurable functions in $L^p$ spaces

Published on 08 Jul 2020 - 9:10

score 88 · Answer 15 · 2020-07-08 19:39:58

88

Views

$f\in L^2[0,1]$ iff $f\in L^1[0,1]$ and there is nondecreasing $g$ with $|\int_a^b f(x)dx|^2 \leq (g(b)-g(a))(b-a)$ for $0\leq a\leq b\leq 1$

Published on 08 Jul 2020 - 19:39

List Question

Twice continuously differentiable function $f:\Bbb R^2\to \Bbb R$ such that $f, f_{xx}, f_{yy}\in L^2$ is bounded

$L^2$ norm of inverse differential operator

If $X_n$ converges to $X$ in $L_p$ and $Y_n$ converges to $Y$ in $L_p$ then $X_n + Y_n $ converges to $X + Y$ in $L_p$

Orthonormal basis in $L^2(\mathbb R)$

About essential range and essential supremum

Prove the relative compactness of a sequence in $L^p$

Weak Bernstein inequality for trigonometric polynomials

Fundamental set in the space of bounded sequences

How to prove $L_{2} ([0,1])$ $\cong$ $L_{2}(\mathbb{R})$

can sequences in $\ell^p$ with $0<p<1$ be multiplied by $n^\alpha$ and still fall in $\ell^1$?

$L^\infty(\mathbb{R}^n)$ function that is also homogenous with degree zero

Understanding proof of Jensen's inequality in Lieb-Loss

Show $l^p$ is not complete with the $q$ norm

multiplication of measurable functions in $L^p$ spaces

$f\in L^2[0,1]$ iff $f\in L^1[0,1]$ and there is nondecreasing $g$ with $|\int_a^b f(x)dx|^2 \leq (g(b)-g(a))(b-a)$ for $0\leq a\leq b\leq 1$

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