10 citations · 19 across the 14 of their papers we have counts for
14 papers
A Lewy theorem for harmonic quasiregular mappings in three-space
David Kalaj, Jian-Feng Zhu
Lewy's classical theorem asserts that a one-to-one planar harmonic mapping has nonvanishing Jacobian. We prove a three-dimensional bounded-distortion analogue: if \[ f:Ω\subset \ma…
Hilbert matrix norms on weighted Bergman spaces: even exponents and a counterexample to the beta formula
Hasi Wulan, Mengmeng Zhou, Jian-Feng Zhu
Let be the weighted Bergman space on the unit disk, where . For , consider the Hilbert matrix operator $\mathcal{H}f(z)=\sum…
Isoperimetric-type inequalities for pluriharmonic functions on the polydisc
Suman Das, Antti Rasila, Jian-Feng Zhu
We prove isoperimetric-type inequalities for complex-valued pluriharmonic functions in the unit polydisc . Denote by and $b^p_{…
The Nitsche--Hopf conjecture for minimal graphs
David Kalaj, Jian-Feng Zhu
We prove the Nitsche--Hopf conjecture for non-parametric minimal graphs over disks. If \(S\) is a minimal graph over a disk of radius \(R\), and if \(ξ\) is the point above the cen…
Improved Hölder regularity for elliptic equations of non-divergence type in the plane
Zhiqiang Hou, Jian-Feng Zhu
In this paper, we obtain an improved Hölder regularity for quasiregular gradient mappings which was studied by Baernstein and Kovalev.
Contraction properties for holomorphic functions via isoperimetric stability on the Bergman ball
David Kalaj, Jian-Feng Zhu
We prove a local contraction property for holomorphic functions that are nearly constant, relating weighted Bergman spaces $A^p_α(\B_n)$ and $A^q_β(\B_n)$. Our approach converts ge…
Composition operators on Bloch and Hardy type spaces
Shaolin Chen, Hidetaka Hamada, Jian-Feng Zhu
The main purpose of this paper is to discuss Hardy type spaces, Bloch type spaces and the composition operators of complex-valued harmonic functions. We first establish a sharp est…
norm estimates of Cauchy transforms on the Dirichlet problem and their applications
Jian-Feng Zhu, Antti Rasila
Denote by the space of the functions on t}he unit disk which are Hölder continuous with the exponent , and denote by th…
-theory for Cauchy-transform on the unit disk
David Kalaj, Petar Melentijević, Jian-Feng Zhu
Let be the unit disk and , where . For , the Cauchy-transform on , denote by $\mathca…
Norm estimates of the Cauchy transform and related operators
Jian-Feng Zhu, David Kalaj
Suppose , where and is the unit disk. Let be the integral operator defined as follows: $\mathfrak{J}_0[f](z)=\int_{\mat…
Boundary Schwarz lemma for harmonic mappings having zero of order
Xiao-Jin Bai, Jie Huang, Jian-Feng Zhu
Suppose is a sense-preserving harmonic mapping of the unit disk such that and has a zero of order at . In this…
Norm estimates of the partial derivatives for harmonic mappings and harmonic quasiregular mappings
Jian-Feng Zhu
Suppose , is a harmonic mapping of the unit disk satisfying is absolutely continuous and , where $\dot{F}(e^{it})=\frac{\ma…
Boundary Schwarz lemma for solutions to non-homogeneous biharmonic equations
Manas Ranjan Mohapatra, Xiantao Wang, Jian-Feng Zhu
In this paper, we establish a boundary Schwarz lemma for solutions to non-homogeneous biharmonic equations.
Neohookean deformations of annuli in the higher dimensional Euclidean space
David Kalaj, Jian-Feng Zhu
Let be an integer and assume that and $\A_\ast = \{y \in \mathbf{R}^n: 1 < |y| < R_\ast\}$ be two annuli in Euclidean space $\mat…