List questions from harmonic-analysis

Published on 30 Mar 2026 - 14:19

84

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How to get $\int_{|t|>\epsilon}\frac{f(x-t)}{t}\ dt=\int_{\epsilon<|t|<R}\frac{f(x-t)-f(x)}{t}\ dt$ where $f$ is smooth and supported on $[-R,R]$?

Published on 25 Dec 2017 - 21:45

191

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How to show that $\lim_{|x|\to\infty}x(\lim_{\epsilon\to 0}\int_{|t|>\epsilon}\frac{f(x-t)}{t}\ dt)=\int_{\bf R}f$?

Published on 26 Dec 2017 - 21:05

297

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Topology on the space of polynomials in $\mathscr{S}'(\mathbb R^n)$

Published on 29 Dec 2017 - 11:43

148

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Showing $ \frac{1}{2\pi i}\int_{\bf R}\frac{f(y)}{y-(x+i\varepsilon)}\ dy=f(x+i\varepsilon)$ in a discussion of Hilbert transform

Published on 01 Jan 2018 - 0:11

321

Views

Weighted Hardy-Littlewood-Sobolev inequality in one dimesion

Published on 02 Apr 2026 - 5:23

96

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Convergence of the $p$-norm of $f+f(x-h)$

Published on 03 Jan 2018 - 2:17

353

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Orthonormality Properties of the Dual Basis in $\mathbb{C}^N$

Published on 06 Jan 2018 - 15:24

72

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Integration of the partial derivative of a homogeneous function of degree zero

Published on 06 Jan 2018 - 17:55

99

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Sum, series and Harmonic numbers

Published on 11 Apr 2026 - 11:16

60

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Tate's thesis: why is the image of $k$ dense in its Pontryagin dual?

Published on 26 Mar 2026 - 22:58

73

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Estimate $f$ from $\widehat{f}$.

Published on 10 Jan 2018 - 1:14

67

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Show that: $\lim\limits_{|x|\to \infty}f_r(x)=0$

Published on 11 Jan 2018 - 13:04

331

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An exercise about BMO from the Grafakos' book

Published on 11 Jan 2018 - 21:36

187

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Show F is the Fourier transform of an integrable function

Published on 11 Apr 2026 - 12:54

List Question

Sums and harmonic series

How to get $\int_{|t|>\epsilon}\frac{f(x-t)}{t}\ dt=\int_{\epsilon<|t|<R}\frac{f(x-t)-f(x)}{t}\ dt$ where $f$ is smooth and supported on $[-R,R]$?

How to show that $\lim_{|x|\to\infty}x(\lim_{\epsilon\to 0}\int_{|t|>\epsilon}\frac{f(x-t)}{t}\ dt)=\int_{\bf R}f$?

Topology on the space of polynomials in $\mathscr{S}'(\mathbb R^n)$

Showing $ \frac{1}{2\pi i}\int_{\bf R}\frac{f(y)}{y-(x+i\varepsilon)}\ dy=f(x+i\varepsilon)$ in a discussion of Hilbert transform

Weighted Hardy-Littlewood-Sobolev inequality in one dimesion

Convergence of the $p$-norm of $f+f(x-h)$

Orthonormality Properties of the Dual Basis in $\mathbb{C}^N$

Integration of the partial derivative of a homogeneous function of degree zero

Sum, series and Harmonic numbers

Tate's thesis: why is the image of $k$ dense in its Pontryagin dual?

Estimate $f$ from $\widehat{f}$.

Show that: $\lim\limits_{|x|\to \infty}f_r(x)=0$

An exercise about BMO from the Grafakos' book

Show F is the Fourier transform of an integrable function

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