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math.CA2026
Fourier decay and endpoint estimates for lacunary maximal operators
Xiaojing Zhou
We study endpoint estimates for lacunary maximal operators associated with compactly supported measures. For every , we construct a compactly supported, absolutely continuo…
math.CA2026
On the Bourgain--Brezis--Mironescu spaces over Carleson tents
Árpád Bényi, Bingyang Hu, Xiaojing Zhou
We introduce Carleson analogs of the Bourgain--Brezis--Mironescu spaces and by measuring mean oscillation over upper Carleson tents. For these spaces, denoted by $B_{\mat…
math.CA2025
From Complex-Analytic Models to Dyadic Methods: A Real-Variable Approach to Hypersingular Operators
Bingyang Hu, Xiaojing Zhou
Motivated by the work of Cheng-Fang-Wang-Yu on the hypersingular Bergman projection, we develop a real-variable framework for hypersingular operators in regimes where strong-type b…