List questions from harmonic-analysis

Published on 27 Mar 2026 - 21:44

101

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Hodge decomposition thm. Why $\Delta(E^p)=d\delta(E^p)\oplus\delta d(E^p)=d(E^{p-1})\oplus\delta(E^{p+1})?$

Published on 26 Mar 2026 - 23:09

52

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The eigenvalue for mollified function

Published on 28 Mar 2016 - 15:51

449

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About Hardy-Littlewood maximal function from Grafakos' "Classical Fourier Analysis"

Published on 28 Mar 2016 - 19:41

2.6k

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Completeness of Schwartz space

Published on 31 Mar 2026 - 5:35

85

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Why is this theorem equivalent to the informal explanation given by Tao?

Published on 31 Mar 2016 - 2:53

98

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If $f_j\to f$ in $L^1(\Bbb R^n)$ then $Tf_j\to Tf$ in $L^{1,\infty}(\Bbb R^n)$

Published on 03 Apr 2016 - 19:36

67

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A Hilbert transform that takes several functions

Published on 04 Apr 2016 - 2:22

85

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If $||g_j-g||_{1,\infty}\to0$, then $||g_j||_{1,\infty}\to||g||_{1,\infty}$

Published on 04 Apr 2016 - 6:18

64

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Estimation with Hölder condition

Published on 28 Mar 2026 - 8:28

191

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Do we have the pointwise bound $\left|\tilde{f}\right| \lesssim_d Mf$?

Published on 07 Apr 2016 - 3:44

511

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Prove that $|k(x)|\le C|x|^{-n}$ under suitable hypothesis on $k\in\mathcal{C}^1(\Bbb R^n\setminus\{0\})$

Published on 25 Mar 2026 - 10:21

111

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How the second and third equalities can be achieved?

Published on 25 Mar 2026 - 20:12

55

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Bounding Fourier coefficients using translates of a function

Published on 10 Apr 2016 - 17:59

165

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Invariant subspace shift operator $\psi H^2$

Published on 25 Mar 2026 - 19:01

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Compostion on $H^2(U)$

Hodge decomposition thm. Why $\Delta(E^p)=d\delta(E^p)\oplus\delta d(E^p)=d(E^{p-1})\oplus\delta(E^{p+1})?$

The eigenvalue for mollified function

About Hardy-Littlewood maximal function from Grafakos' "Classical Fourier Analysis"

Completeness of Schwartz space

Why is this theorem equivalent to the informal explanation given by Tao?

If $f_j\to f$ in $L^1(\Bbb R^n)$ then $Tf_j\to Tf$ in $L^{1,\infty}(\Bbb R^n)$

A Hilbert transform that takes several functions

If $||g_j-g||_{1,\infty}\to0$, then $||g_j||_{1,\infty}\to||g||_{1,\infty}$

Estimation with Hölder condition

Do we have the pointwise bound $\left|\tilde{f}\right| \lesssim_d Mf$?

Prove that $|k(x)|\le C|x|^{-n}$ under suitable hypothesis on $k\in\mathcal{C}^1(\Bbb R^n\setminus\{0\})$

How the second and third equalities can be achieved?

Bounding Fourier coefficients using translates of a function

Invariant subspace shift operator $\psi H^2$

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