Question

An estimate in the introduction of the Hilbert transform in Grafakos's Classical Fourier Analysis

score 151 · Answer 1 · 2026-03-27 08:21:53

151

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An estimate in the introduction of the Hilbert transform in Grafakos's Classical Fourier Analysis

Published on 27 Mar 2026 - 8:21

score 115 · Answer 2 · 2026-03-17 13:30:59

115

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Show that $x\longmapsto \int_{\mathbb R^n}\frac{f(y)}{|x-y|^{n-\alpha }}dy$ is integrable.

Published on 17 Mar 2026 - 13:30

score 74 · Answer 3 · 2026-03-27 10:19:38

74

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Verifying that translation by $h$ in time is the same as modulating by $-h$ in frequency (Fourier Analysis)

Published on 27 Mar 2026 - 10:19

score 216 · Answer 4 · 2026-03-25 15:40:29

216

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Seeking an example of Schwartz function $f$ such that $ \int_{\bf R}\left|\frac{f(x-y)}{y}\right|\ dy=\infty$

Published on 25 Mar 2026 - 15:40

score 916 · Answer 5 · 2026-03-27 04:13:00

916

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Computing Pontryagin Duals

Published on 27 Mar 2026 - 4:13

score 102 · Answer 6 · 2026-03-19 02:17:44

102

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Understanding Book Proof that $[-2 \pi i x f(x)]^{\wedge}(\xi) = {d \over d\xi} \widehat{f}(\xi)$

Published on 19 Mar 2026 - 2:17

score 64 · Answer 7 · 2026-03-20 03:56:12

64

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Expanding $\left| [\widehat{f}( \xi + h) - \widehat{f}( \xi)]/h - [- 2 \pi i f(x)]^{\wedge}(\xi) \right|$ into one integral

Published on 20 Mar 2026 - 3:56

score 1.1k · Answer 8 · 2026-03-22 08:05:31

1.1k

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When does $\lim_{n\to\infty}f(x+\frac{1}{n})=f(x)$ a.e. fail

Published on 22 Mar 2026 - 8:05

score 38 · Answer 9 · 2026-03-21 10:08:19

38

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The linear partial differential operator with constant coefficient has no solution

Published on 21 Mar 2026 - 10:08

score 299 · Answer 10 · 2026-03-19 04:31:27

299

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Show $\widehat{\mathbb{Z}}$ is isomorphic to $S^1$

Published on 19 Mar 2026 - 4:31

score 68 · Answer 11 · 2026-03-22 09:11:28

68

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The Fourier transform in the sense of tempered distribution is not a function

Published on 22 Mar 2026 - 9:11

score 52 · Answer 12 · 2026-03-24 22:57:37

52

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Riesz potential $I_{\alpha}\phi\notin L^2$ if $\frac{n}{2}<\alpha<n,$

Published on 24 Mar 2026 - 22:57

score 233 · Answer 13 · 2026-03-25 23:39:10

233

Views

Representation of projection valued measures as operator

Published on 25 Mar 2026 - 23:39

score 843 · Answer 14 · 2026-03-26 21:46:11

843

Views

Finding an harmonic function

Published on 26 Mar 2026 - 21:46

score 1.6k · Answer 15 · 2026-03-25 05:56:16

1.6k

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Hardy-Littlewood maximal function not integrable in B(0,1)

Published on 25 Mar 2026 - 5:56

List Question

An estimate in the introduction of the Hilbert transform in Grafakos's Classical Fourier Analysis

Show that $x\longmapsto \int_{\mathbb R^n}\frac{f(y)}{|x-y|^{n-\alpha }}dy$ is integrable.

Verifying that translation by $h$ in time is the same as modulating by $-h$ in frequency (Fourier Analysis)

Seeking an example of Schwartz function $f$ such that $ \int_{\bf R}\left|\frac{f(x-y)}{y}\right|\ dy=\infty$

Computing Pontryagin Duals

Understanding Book Proof that $[-2 \pi i x f(x)]^{\wedge}(\xi) = {d \over d\xi} \widehat{f}(\xi)$

Expanding $\left| [\widehat{f}( \xi + h) - \widehat{f}( \xi)]/h - [- 2 \pi i f(x)]^{\wedge}(\xi) \right|$ into one integral

When does $\lim_{n\to\infty}f(x+\frac{1}{n})=f(x)$ a.e. fail

The linear partial differential operator with constant coefficient has no solution

Show $\widehat{\mathbb{Z}}$ is isomorphic to $S^1$

The Fourier transform in the sense of tempered distribution is not a function

Riesz potential $I_{\alpha}\phi\notin L^2$ if $\frac{n}{2}<\alpha<n,$

Representation of projection valued measures as operator

Finding an harmonic function

Hardy-Littlewood maximal function not integrable in B(0,1)

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