List questions from harmonic-analysis

Published on 13 Apr 2026 - 10:57

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If $f\in C([a,b])$, $V(f^2;[a,b])<\infty$, then $V_2(f;[a,b]) \leq C(V(f^2;[a,b])+\|f\|_\infty^2)$

Published on 16 Apr 2026 - 4:25

29

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The proof for an integral inequality

Published on 25 Mar 2026 - 16:45

45

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Estimate the value of a nonnegative harmonic function

Published on 11 Apr 2026 - 18:55

59

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$G$ be loacally compact abelian group with $G,\hat{G}$ both sigma compact. Let $f\in L^2(G)$ and $\psi_n(x)=\int_{C_n}\hat{f}(\chi)\chi(x)\ d\chi$.

Published on 16 Apr 2026 - 5:52

72

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why does the Fourier algebra $A(G)$ consits precisely with the set of matrix coefficients of the LRR?

Published on 15 Apr 2026 - 13:20

106

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Why $\{x: Mf(x) > \lambda\} $ is open for any $\lambda \in \mathbb{R}$?

Published on 14 Apr 2026 - 12:40

115

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Bourgain's paper on kakeya conjecture

Published on 16 Apr 2026 - 22:31

40

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Existence of $h\in\mathcal{F}(C_c^{\infty})$ such that $\int_{\mathbb{R}^{d}}h(x)\mathrm{d}x=1$.

Published on 12 Apr 2026 - 12:35

68

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Pontryagin dual and unitary dual of abelian group homeomorphic?

Published on 14 Apr 2026 - 0:04

91

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The calculation of dyadic addition

Published on 11 Apr 2026 - 5:40

112

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The space of holomorphic polynomials is dense on the weighted Bergman space $\mathcal A^2(\mathbb D)$

Published on 11 Apr 2026 - 23:32

201

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Exercise on harmonic functions

Published on 12 Apr 2026 - 0:45

445

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Royal road to Abstract Harmonic Analysis?

Published on 11 Apr 2026 - 19:29

105

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Exercise on elliptic PDE

Published on 16 Apr 2026 - 9:45

List Question

$m(\xi)=(-1)^{[\xi^2]}$ is not a Fourier multiplier

If $f\in C([a,b])$, $V(f^2;[a,b])<\infty$, then $V_2(f;[a,b]) \leq C(V(f^2;[a,b])+\|f\|_\infty^2)$

The proof for an integral inequality

Estimate the value of a nonnegative harmonic function

$G$ be loacally compact abelian group with $G,\hat{G}$ both sigma compact. Let $f\in L^2(G)$ and $\psi_n(x)=\int_{C_n}\hat{f}(\chi)\chi(x)\ d\chi$.

why does the Fourier algebra $A(G)$ consits precisely with the set of matrix coefficients of the LRR?

Why $\{x: Mf(x) > \lambda\} $ is open for any $\lambda \in \mathbb{R}$?

Bourgain's paper on kakeya conjecture

Existence of $h\in\mathcal{F}(C_c^{\infty})$ such that $\int_{\mathbb{R}^{d}}h(x)\mathrm{d}x=1$.

Pontryagin dual and unitary dual of abelian group homeomorphic?

The calculation of dyadic addition

The space of holomorphic polynomials is dense on the weighted Bergman space $\mathcal A^2(\mathbb D)$

Exercise on harmonic functions

Royal road to Abstract Harmonic Analysis?

Exercise on elliptic PDE

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