In this paper,Schwarz-type lemmas for different classes of quaternion functions are obtained.Firstly,some properties of symmetric points are given.Secondly,the Schwarz-type lemma and the Schwarz-Pick-type theorem for ...In this paper,Schwarz-type lemmas for different classes of quaternion functions are obtained.Firstly,some properties of symmetric points are given.Secondly,the Schwarz-type lemma and the Schwarz-Pick-type theorem for quaternion regular functions are obtained.Finally,the Schwarz-type lemma for quaternion k-regular functions is derived.展开更多
The power series expansions of normalized biholomorphic convex mappings on the Reinhardt domain are studied.It is proved that the first (k+1 ) terms ofthe expansions of the jth component fj of such a map / depend only...The power series expansions of normalized biholomorphic convex mappings on the Reinhardt domain are studied.It is proved that the first (k+1 ) terms ofthe expansions of the jth component fj of such a map / depend only on zj for 1≤j≤n,where k is the natural number that satisfies k<p≤k+1.When p∞,this gives the result on the unit polydisc obtained by Sulfridge in 1970.展开更多
In this article we discuss the explicit solvability of both Schwarz boundary value problem and Riemann-Hilbert boundary value problem on a half hexagon in the complex plane. Schwarz-type and Pompeiu-type integrals are...In this article we discuss the explicit solvability of both Schwarz boundary value problem and Riemann-Hilbert boundary value problem on a half hexagon in the complex plane. Schwarz-type and Pompeiu-type integrals are obtained. The boundary behavior of these operators is discussed. Finally, we investigate the Schwarz problem and the Riemann-Hilbert problem for inhomogeneous Cauchy-Riemann equations.展开更多
Let R_I(m,n) be the classical domain of type I in C^(m×n)with 1≤m≤n.We obtain the optimal estimates of the eigenvalues of the Fréchet derivative Df(Z) at a smooth boundary fixed point Z of R_I(m,n)for a ho...Let R_I(m,n) be the classical domain of type I in C^(m×n)with 1≤m≤n.We obtain the optimal estimates of the eigenvalues of the Fréchet derivative Df(Z) at a smooth boundary fixed point Z of R_I(m,n)for a holomorphic self-mapping f of R_L(m,n).We provide a necessary and sufficient condition such that the boundary points of R_I(m,n) are smooth,and give some properties of the smooth boundary points of R_L(m,n).Our results extend the classical Schwarz lemma at the boundary of the unit disk △ to R_I(m,n),which may be applied to get some optimal estimates in several complex variables.展开更多
基金supported by the Innovation Foundation of the School of Mathematical Sciences in Hebei Normal University in 2025(ycxzzbs202503)the NSF of Hebei Province(A2023205006,A2022208007,A2023205045,A2024208005)+2 种基金the Hebei Research Center of the Basic Discipline Pure Mathematics,the Key Development Foundation of Hebei Normal University(L2024ZD08)the NSFC(12431005)the Funding Project of Central Guidance for Local Scientific and Technological Development(246Z7608G).
文摘In this paper,Schwarz-type lemmas for different classes of quaternion functions are obtained.Firstly,some properties of symmetric points are given.Secondly,the Schwarz-type lemma and the Schwarz-Pick-type theorem for quaternion regular functions are obtained.Finally,the Schwarz-type lemma for quaternion k-regular functions is derived.
基金Project supported in part by the National Natural Science Foundation of China.
文摘The power series expansions of normalized biholomorphic convex mappings on the Reinhardt domain are studied.It is proved that the first (k+1 ) terms ofthe expansions of the jth component fj of such a map / depend only on zj for 1≤j≤n,where k is the natural number that satisfies k<p≤k+1.When p∞,this gives the result on the unit polydisc obtained by Sulfridge in 1970.
文摘In this article we discuss the explicit solvability of both Schwarz boundary value problem and Riemann-Hilbert boundary value problem on a half hexagon in the complex plane. Schwarz-type and Pompeiu-type integrals are obtained. The boundary behavior of these operators is discussed. Finally, we investigate the Schwarz problem and the Riemann-Hilbert problem for inhomogeneous Cauchy-Riemann equations.
基金National Natural Science Foundation of China(Grant Nos. 11571105 and 11471111)Natural Science Foundation of Zhejiang Province(Grant No.LY14A010017)
文摘Let R_I(m,n) be the classical domain of type I in C^(m×n)with 1≤m≤n.We obtain the optimal estimates of the eigenvalues of the Fréchet derivative Df(Z) at a smooth boundary fixed point Z of R_I(m,n)for a holomorphic self-mapping f of R_L(m,n).We provide a necessary and sufficient condition such that the boundary points of R_I(m,n) are smooth,and give some properties of the smooth boundary points of R_L(m,n).Our results extend the classical Schwarz lemma at the boundary of the unit disk △ to R_I(m,n),which may be applied to get some optimal estimates in several complex variables.
