Zhenghui Huo

Journal Article Canadian Journal of Mathematics · January 1, 2024 We study the Lp regularity of the Bergman projection P over the symmetrized polydisc in ℂn. We give a decomposition of the Bergman projection on the polydisc and obtain an operator equivalent to the Bergman projection over antisymmetric function spaces. Us ... Full text Cite

Zero products of Toeplitz operators on Reinhardt domains

Journal Article Canadian Mathematical Bulletin · March 8, 2022 Let O be a bounded Reinhardt domain in Cn and 1, . . . m be finite sums of bounded quasi-homogeneous functions.We show that if the product of Toeplitz operators Tm T1 = 0 on the Bergman space on O, then j = 0 for some j. ... Full text Cite

Dyadic Carleson embedding and sparse domination of weighted composition operators on strictly pseudoconvex domains

Journal Article Bulletin des Sciences Mathematiques · December 1, 2021 In this paper, we study the behavior of the weighted composition operators acting on Bergman spaces defined on strictly pseudoconvex domains via the sparse domination technique from harmonic analysis. As a byproduct, we also prove a weighted type estimate ... Full text Cite

Bekollé-Bonami estimates on some pseudoconvex domains

Journal Article Bulletin des Sciences Mathematiques · September 1, 2021 We establish a weighted Lp norm estimate for the Bergman projection for a class of pseudoconvex domains. We obtain an upper bound for the weighted Lp norm when the domain is, for example, a bounded smooth strictly pseudoconvex domain, a pseudoconvex domain ... Full text Cite

A Békollè–Bonami Class of Weights for Certain Pseudoconvex Domains

Journal Article Journal of Geometric Analysis · June 1, 2021 Featured Publication We prove the weighted Lp regularity of the ordinary Bergman projection on certain pseudoconvex domains where the weight belongs to an appropriate generalization of the Békollè–Bonami class. The main tools used are estimates on the Bergman kernel obtained b ... Full text Cite

Weighted estimates for the Bergman projection on the Hartogs triangle

Journal Article Journal of Functional Analysis · November 15, 2020 Featured Publication We apply modern techniques of dyadic harmonic analysis to obtain sharp estimates for the Bergman projection in weighted Bergman spaces. Our main theorem focuses on the Bergman projection on the Hartogs triangle. The estimates of the operator norm are in te ... Full text Cite

Weak-type estimates for the Bergman projection on the polydisc and the Hartogs triangle

Journal Article Bulletin of the London Mathematical Society · October 1, 2020 Featured Publication In this paper, we investigate the weak-type regularity of the Bergman projection. The two domains we focus on are the polydisc and the Hartogs triangle. For the polydisc, we provide a proof that the weak-type behavior is of ‘ (Formula presented.) ’ type. T ... Full text Cite

L^p estimates for the bergman projection on some reinhardt domains

Journal Article Proceedings of the American Mathematical Society · January 1, 2018 Featured Publication We obtain Lp regularity for the Bergman projection on some Reinhardt domains. We start with a bounded initial domain Ω with some symmetry properties and generate successor domains in higher dimensions. We prove: If the Bergman kernel on Ω satisfies appropr ... Full text Cite

The Bergman Kernel on Some Hartogs Domains

Journal Article Journal of Geometric Analysis · January 1, 2017 Featured Publication We obtain new explicit formulas for the Bergman kernel function on two families of Hartogs domains. To do so, we first compute the Bergman kernels on the slices of these Hartogs domains with some coordinates fixed, evaluate these kernel functions at certai ... Full text Cite

Proper holomorphic maps from the unit disk to some unit ball

Journal Article Proceedings of the American Mathematical Society · January 1, 2017 We study proper rational maps from the unit disk to balls in higher dimensions. After gathering some known results, we study the moduli space of unitary equivalence classes of polynomial proper maps from the disk to a ball, and we establish a normal form f ... Full text Cite