Hao Zhang

activity

20242026

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4 papers · 1 filter

math.FA2026

Dimension-free Riesz transform estimates on biased hypercubes via non-tracial baby Fock models

Hun Hee Lee, Zhendong Xu, Sang-gyun Youn +1

We study dimension-free Riesz transform estimates on hypercubes equipped with non-uniform product measures. For $2 \leq p < \infty$ , we prove a dimension-free Meyer inequality for the…

math.FA2026

The Endpoint Fractional Riesz Estimate on the Hamming Cube

Zhendong Xu, Hao Zhang

Let $1 < p < 2$ and $D_{j}$ be the discrete partial derivative on the Hamming cube $Ω_{n} = {- 1, 1}^{n}$ . Let $Δ = \sum_{j = 1}^{n} D_{j}$ be the discrete Laplacian. We prove the endpoint inequali…

math.FA2026

Hypercontractivity for a family of quantum Ornstein-Uhlenbeck semigroups

Longfa Sun, Zhendong Xu, Hao Zhang

We show that a family of quantum Ornstein-Uhlenbeck semigroups is hypercontractive. We also obtain the optimal order of the optimal time up to a constant. The main ingredient of ou…

math.NT2026

Average first-passage times for character sums

Quanyu Tang, Hao Zhang

Let $ε > 0$ and, for an odd prime $p$ , set $S_{ℓ} (p) := n \leq ℓ \sum (\frac{n}{p}) .$ Define the first-passage time $$ f_\varepsilon(p):=\min\{\ell\ge 1:\ S…