Question

Brezis' Exercise 5.30.4: an orthonormal basis of $L^2(0, 1)$

score 49 · Answer 1 · 2026-04-06 06:18:23

49

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Brezis' Exercise 5.30.4: an orthonormal basis of $L^2(0, 1)$

Published on 06 Apr 2026 - 6:18

score 103 · Answer 2 · 2026-04-09 02:04:34

103

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Possible Frechet-Kolmogorov compactness theorem equivalent in $L^\infty$?

Published on 09 Apr 2026 - 2:04

score 45 · Answer 3 · 2023-05-18 04:30:04

45

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If $1/m$ is a Fourier multiplier in $L^p,$ then is $1/(1+m)$ also a Fourier multiplier?

Published on 18 May 2023 - 4:30

score 44 · Answer 4 · 2026-04-07 16:14:50

44

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Any constant function is a Fourier Multiplier in $L^p(\mathbb{R}^n)$?

Published on 07 Apr 2026 - 16:14

score 58 · Answer 5 · 2026-04-09 11:09:52

58

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Norm of an operator

Published on 09 Apr 2026 - 11:09

score 91 · Answer 6 · 2023-05-19 08:06:14

91

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Embeddings of $L^p$ spaces over the range $0 < p < \infty$

Published on 19 May 2023 - 8:06

score 138 · Answer 7 · 2023-05-20 12:53:52

138

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Find a subspace of $L^2([0,1])$ which is dense in $L^p([0,1])$ for all $p<2$ but not in $L^2([0,1])$

Published on 20 May 2023 - 12:53

score 52 · Answer 8 · 2023-05-21 21:49:07

52

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If $\lambda(f_n^{-1}(U))$ converges for all measurable sets $U,$ does $\{f_n\}$ have a convergent subsequence?

Published on 21 May 2023 - 21:49

score 142 · Answer 9 · 2026-03-26 12:58:08

142

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How can I prove $L^p$ continuity of the left-shift operator?

Published on 26 Mar 2026 - 12:58

score 32 · Answer 10 · 2023-05-24 16:53:08

32

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If $\lambda(f_n^{-1}(A) \cap g_n^{-1}(B))$ converges for all measurable sets $A, B,$ do $f_n, g_n$ converge under $\lambda$?

Published on 24 May 2023 - 16:53

score 41 · Answer 11 · 2026-03-27 23:13:53

41

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For which values of the parameter $r$ the operator is compact?

Published on 27 Mar 2026 - 23:13

score 44 · Answer 12 · 2026-03-25 11:20:20

44

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Showing that $\{\varphi_{m,n} \}_{m \geq 1, n \geq 1}$ is an orthonormal basis for $L^2((a,b) \times (a,b)).$

Published on 25 Mar 2026 - 11:20

score 51 · Answer 13 · 2026-03-27 02:37:44

51

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How to prove $\sup_{t\in [a, b]} \int_{\mathbb R^d} |f_t (x)|^p \, \mathrm d x<\infty$ in higher dimension?

Published on 27 Mar 2026 - 2:37

score 46 · Answer 14 · 2023-05-29 17:27:06

46

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Is the span of a in infinite list of orthogonal vectors in $L^2$ closed?

Published on 29 May 2023 - 17:27

score 75 · Answer 15 · 2023-06-02 02:32:21

75

Views

Bounding $L^2$ norm by $L^\infty$ norm

Published on 02 Jun 2023 - 2:32

List Question

Brezis' Exercise 5.30.4: an orthonormal basis of $L^2(0, 1)$

Possible Frechet-Kolmogorov compactness theorem equivalent in $L^\infty$?

If $1/m$ is a Fourier multiplier in $L^p,$ then is $1/(1+m)$ also a Fourier multiplier?

Any constant function is a Fourier Multiplier in $L^p(\mathbb{R}^n)$?

Norm of an operator

Embeddings of $L^p$ spaces over the range $0 < p < \infty$

Find a subspace of $L^2([0,1])$ which is dense in $L^p([0,1])$ for all $p<2$ but not in $L^2([0,1])$

If $\lambda(f_n^{-1}(U))$ converges for all measurable sets $U,$ does $\{f_n\}$ have a convergent subsequence?

How can I prove $L^p$ continuity of the left-shift operator?

If $\lambda(f_n^{-1}(A) \cap g_n^{-1}(B))$ converges for all measurable sets $A, B,$ do $f_n, g_n$ converge under $\lambda$?

For which values of the parameter $r$ the operator is compact?

Showing that $\{\varphi_{m,n} \}_{m \geq 1, n \geq 1}$ is an orthonormal basis for $L^2((a,b) \times (a,b)).$

How to prove $\sup_{t\in [a, b]} \int_{\mathbb R^d} |f_t (x)|^p \, \mathrm d x<\infty$ in higher dimension?

Is the span of a in infinite list of orthogonal vectors in $L^2$ closed?

Bounding $L^2$ norm by $L^\infty$ norm

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