List questions from harmonic-analysis

Published on 25 Mar 2026 - 12:13

476

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Is the truncated Hardy-Littlewood maximal function of an $L^1$ function also in $L^1$?

Published on 09 Aug 2018 - 8:31

166

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An interpolation inequality for Fourier cosine series

Published on 26 Mar 2026 - 23:11

856

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Inverse Hausdorff Young

Published on 26 Mar 2026 - 21:25

286

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Inverse of a Fourier Transform is $L^1 \cap L^{\infty}$

Published on 23 Mar 2026 - 20:58

575

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Irrep. of SU(2) and Laplace Eigenspaces

Published on 25 Mar 2026 - 6:10

199

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If $f\in L^1(\mathbb{T})$ is such that $\forall n<0, \hat{f}(n)=0$, does the Fourier series of $f$ converges in $L^1(\mathbb{T})$ norm to $f$?

Published on 26 Mar 2026 - 23:10

211

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Regarding convolution of Fejér kernel with a Lipschitz function

Published on 27 Mar 2026 - 22:20

105

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An inequality about Besov norm: transfer the index $s$ to the multiplier $\langle \xi \rangle^s$

Published on 16 Aug 2018 - 12:17

54

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Regarding Fourier coefficients

Published on 18 Aug 2018 - 19:27

44

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Let $f\in L_2(\mathbb R)$ be a function. Is $\displaystyle\sum_{k\in\mathbb{Z}}|f(k)|^2<\infty $?

Published on 19 Aug 2018 - 3:36

98

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Suppose $f\in L_2(\mathbb R)$ and $f$ is a continuous function on $\mathbb R$. Is $\displaystyle\sum_{k\in\mathbb{Z}}|f(k)|^2<\infty $?

Published on 19 Aug 2018 - 4:39

159

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How to derive Riesz transform from its Fourier transform?

Published on 20 Aug 2018 - 7:09

162

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Hardy-littlewood maximal inequality for doubling measures

Published on 20 Aug 2018 - 20:13

80

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Integration of a complex exponential

Published on 21 Aug 2018 - 21:25

List Question

Convolution by $\log$ maps $\mathrm{L}^1$ into $\mathrm{BMO}$

Is the truncated Hardy-Littlewood maximal function of an $L^1$ function also in $L^1$?

An interpolation inequality for Fourier cosine series

Inverse Hausdorff Young

Inverse of a Fourier Transform is $L^1 \cap L^{\infty}$

Irrep. of SU(2) and Laplace Eigenspaces

If $f\in L^1(\mathbb{T})$ is such that $\forall n<0, \hat{f}(n)=0$, does the Fourier series of $f$ converges in $L^1(\mathbb{T})$ norm to $f$?

Regarding convolution of Fejér kernel with a Lipschitz function

An inequality about Besov norm: transfer the index $s$ to the multiplier $\langle \xi \rangle^s$

Regarding Fourier coefficients

Let $f\in L_2(\mathbb R)$ be a function. Is $\displaystyle\sum_{k\in\mathbb{Z}}|f(k)|^2<\infty $?

Suppose $f\in L_2(\mathbb R)$ and $f$ is a continuous function on $\mathbb R$. Is $\displaystyle\sum_{k\in\mathbb{Z}}|f(k)|^2<\infty $?

How to derive Riesz transform from its Fourier transform?

Hardy-littlewood maximal inequality for doubling measures

Integration of a complex exponential

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