List questions from harmonic-analysis

Published on 26 Mar 2026 - 16:06

243

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$L^{1,w}$-norm of the Hardy-Littlewood maximal operator

Published on 19 Nov 2017 - 14:03

269

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Fourier transform: can we expect $\|\mathcal F( | \mathcal F f |)\|_{L^\infty} \lesssim \|f\|_{L^\infty}$?

Published on 19 Nov 2017 - 21:39

2.9k

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Product $u v$ of harmonic functions is harmonic if $\langle \nabla u, \nabla v \rangle$ is $\equiv 0$ everywhere

Published on 04 Apr 2026 - 20:35

271

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Does Hilbert transform commute with integral?

Published on 25 Mar 2026 - 13:32

305

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An inequality by using general Hölder's inequality

Published on 26 Mar 2026 - 21:07

528

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Intuition regrading the weak $L^p$ functions

Published on 22 Mar 2026 - 20:17

137

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If $\Delta u(x,y)=0,\ \ \text{in}\ B,\ \ \ u(x,y)=\sin(x)\ \ \text{on}\ \partial B$ then compute $u(0,0)$

Published on 05 Apr 2026 - 1:19

524

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Intuition of the Lorentz norm in an Wikipedia article

Published on 25 Mar 2026 - 19:05

616

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Proving that : $ \left|\int_a^b\frac{\widehat{f}(\xi)}{\xi}d\xi\right|\le 4 \|f\|_1$ for all $a,b$ and all $f$

Published on 24 Nov 2017 - 22:09

398

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Finding Calderon-Zygmund decomposition of a function

Published on 25 Mar 2026 - 13:42

572

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Proving Hilbert transform is skew-adjoint

Published on 25 Mar 2026 - 13:32

878

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Proving Cotlar's Identity of Hilbert transform

Published on 25 Mar 2026 - 13:42

133

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Caccioppoli type inequality for harmonic function

Published on 05 Apr 2026 - 1:14

72

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Tiling by Translation and Orthonormal Basis

Published on 26 Mar 2026 - 9:39

List Question

Spherical Harmonics expansion for $f\in L^{2}(S^{n-1})$.

$L^{1,w}$-norm of the Hardy-Littlewood maximal operator

Fourier transform: can we expect $\|\mathcal F( | \mathcal F f |)\|_{L^\infty} \lesssim \|f\|_{L^\infty}$?

Product $u v$ of harmonic functions is harmonic if $\langle \nabla u, \nabla v \rangle$ is $\equiv 0$ everywhere

Does Hilbert transform commute with integral?

An inequality by using general Hölder's inequality

Intuition regrading the weak $L^p$ functions

If $\Delta u(x,y)=0,\ \ \text{in}\ B,\ \ \ u(x,y)=\sin(x)\ \ \text{on}\ \partial B$ then compute $u(0,0)$

Intuition of the Lorentz norm in an Wikipedia article

Proving that : $ \left|\int_a^b\frac{\widehat{f}(\xi)}{\xi}d\xi\right|\le 4 \|f\|_1$ for all $a,b$ and all $f$

Finding Calderon-Zygmund decomposition of a function

Proving Hilbert transform is skew-adjoint

Proving Cotlar's Identity of Hilbert transform

Caccioppoli type inequality for harmonic function

Tiling by Translation and Orthonormal Basis

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