10 citations · 19 across the 14 of their papers we have counts for
12 papers · 1 filter
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…
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…
-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…