Xianghong Chen

activity

20122025

most citedConvolution Powers of Salem Measures with Applications

17 citations · 22 across the 12 of their papers we have counts for

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9 papers · 1 filter

math.CA2023

On the generalized Hausdorff dimension of Besicovitch sets

Xianghong Chen, Lixin Yan, Yue Zhong

Keich (1999) showed that the sharp gauge function for the generalized Hausdorff dimension of Besicovitch sets in $R^{2}$ is between $r^{2} lo g 1/ r$ and $r^2(\log 1/r) (\log\log…

math.CA2023

On smoothing estimates for Schrödinger equations on product spaces $T^{m} \times R^{n}$

Xianghong Chen, Zihua Guo, Minxing Shen +1

Let $Δ_{T^{m} \times R^{n}}$ denote the Laplace-Beltrami operator on the product spaces $T^{m} \times R^{n}$ . In this article we show that $$ \left\|e^{it…

math.CA2018

Almost everywhere divergence of spherical harmonic expansions and equivalence of summation methods

Xianghong Chen, Dashan Fan, Juan Zhang

We show that there exists an integrable function on the $n$ -sphere $(n \geq 2)$ , whose Cesàro (C, $\frac{n - 1}{2}$ ) means with respect to the spherical harmonic expansion diverge unbou…

math.CA2017

Asymptotics of signed Bernoulli convolutions scaled by multinacci numbers

Xianghong Chen, Tian-You Hu

We study the signed Bernoulli convolution $ν_{β}^{(n)} = *_{j = 1}^{n} (\frac{1}{2} δ_{β^{- j}} - \frac{1}{2} δ_{- β^{- j}}), n \geq 1$ where $β > 1$ satisfies $β^{m} = β^{m - 1} + \dots + β + 1$ for…

math.CA2017

Restriction of the Fourier transform to some oscillating curves

Xianghong Chen, Dashan Fan, Lifeng Wang

Let $ϕ$ be a smooth function on a compact interval $I$ . Let $γ (t) = (t, t^{2}, \dots, t^{n - 1}, ϕ (t)) .$ In this paper, we show that $$\left(\int_I \big|\hat f(γ(t))\big|^q \b…

math.CA2016

On almost everywhere divergence of Bochner-Riesz means on compact Lie groups

Xianghong Chen, Dashan Fan

Let $G$ be a connected, simply connected, compact semisimple Lie group of dimension $n$ . It has been shown by Clerc \cite{Clerc1974} that, for any $f \in L^{1} (G)$ , the Bochner-Riesz…

math.CA2015★ 17 cited

Convolution Powers of Salem Measures with Applications

Xianghong Chen, Andreas Seeger

We study the regularity of convolution powers for measures supported on Salem sets, and prove related results on Fourier restriction and Fourier multipliers. In particular we show…

math.CA2013★ 3 cited

Sets of Salem type and sharpness of the $L^{2}$ -Fourier restriction theorem

Xianghong Chen

We construct Salem sets on the real line with endpoint Fourier decay and near-endpoint regularity properties. This complements a result of Łaba and Pramanik, who obtained near-endp…

math.CA2012★ 1 cited

A Fourier restriction theorem based on convolution powers

Xianghong Chen

We prove a Fourier restriction estimate under the assumption that certain convolution power of the measure admits an $r$ -integrable density.

On the generalized Hausdorff dimension of Besicovitch sets

On smoothing estimates for Schrödinger equations on product spaces Tm×Rn

Almost everywhere divergence of spherical harmonic expansions and equivalence of summation methods

Asymptotics of signed Bernoulli convolutions scaled by multinacci numbers

Restriction of the Fourier transform to some oscillating curves

On almost everywhere divergence of Bochner-Riesz means on compact Lie groups

Convolution Powers of Salem Measures with Applications

Sets of Salem type and sharpness of the L2-Fourier restriction theorem

A Fourier restriction theorem based on convolution powers

On smoothing estimates for Schrödinger equations on product spaces $T^{m} \times R^{n}$

Sets of Salem type and sharpness of the $L^{2}$ -Fourier restriction theorem