1 citations · 1 across the 5 of their papers we have counts for
7 papers
A quantitative form of the planar Falconer distance theorem
Guozheng Cheng, Xiang Fang, Menghan Li +2
We give a quantitative planar form of a multiscale argument for Falconer's distance problem. For every , we obtain a positive lower bound for the Lebesgue measure of the dis…
Strict correlation-dimension drop for quartic Salem Bernoulli convolutions
Guozheng Cheng, Xiang Fang, Xueqing Ma +1
For every quartic Salem number , we prove that the Bernoulli convolution with equal weights has correlation dimension strictly less than one. In particular,…
Canonical Mandelbrot Cascades on Curves Are Rajchman
Yin Cai, Guozheng Cheng, Xiang Fang +3
We settle the Rajchman problem for canonical scalar dyadic Mandelbrot cascades at the minimal Kahane--Peyrière integrability threshold. If is the cascade on , then $\wid…
Exact Fourier dimensions of dyadic Mandelbrot cascades under minimal integrability
Yin Cai, Guozheng Cheng, Xiang Fang +3
We determine the Fourier dimension of dyadic Mandelbrot cascades under the minimal Kahane-Peyriere integrability condition. The interval theorem is proved in a vector-valued dyadic…
A Gaussian version of Littlewood's theorem on random power series
Guozheng Cheng, Xiang Fang, Kunyu Guo +1
We prove a Littlewood-type theorem on random analytic functions for not necessarily independent Gaussian processes. We show that if we randomize a function in the Hardy space $H^2(…
Random weighted shifts
Guozheng Cheng, Xiang Fang, Sen Zhu
In this paper we initiate the study of a fundamental yet untapped random model of non-selfadjoint, bounded linear operators acting on a separable complex Hilbert space. We replace…
Three Remarks on Carleson Measures for Dirichlet Space
Guozheng Cheng, Xiang Fang, Zipeng Wang +1
In this paper, we prove that all doubling measures on the unit disk are Carleson measures for the standard Dirichlet space . The proof has three ingredien…