期刊：
Journal of Mathematical Analysis and Applications,2020年486(2):123920 ISSN：0022-247X
通讯作者：
Ponnusamy, Saminathan
作者机构：
[Chen, Shaolin] Hengyang Normal Univ, Coll Math & Stat, Hengyang 421008, Hunan, Peoples R China.;[Ponnusamy, Saminathan] Indian Inst Technol Madras, Dept Math, Chennai 600036, Tamil Nadu, India.
通讯机构：
[Ponnusamy, Saminathan] I;Indian Inst Technol Madras, Dept Math, Chennai 600036, Tamil Nadu, India.
摘要：
Let (D) over bar be the closure of the unit disk D in the complex plane C and g be a continuous function in (D) over bar. In this paper, we discuss some characterizations of elliptic mappings f satisfying the Poisson's equation Delta f = g in D, and then establish some sharp distortion theorems on elliptic mappings with the finite perimeter and the finite radial length, respectively. The obtained results are the extension of the corresponding classical results. (C) 2020 Elsevier Inc. All rights reserved.
期刊：
ANNALES ACADEMIAE SCIENTIARUM FENNICAE-MATHEMATICA,2019年44(1):427-448 ISSN：1239-629X
通讯作者：
Chen, Shaolin
作者机构：
[Chen, Shaolin] Hengyang Normal Univ, Coll Math & Stat, Hengyang 421008, Hunan, Peoples R China;[Rasila, Antti] Guangdong Technion Israel Inst Technol, Coll Sci, 241 Daxue Rd, Shantou 515063, Guangdong, Peoples R China;[Vuorinen, Matti] Univ Turku, Dept Math & Stat, Turku 20014, Finland
通讯机构：
[Chen, Shaolin] H;Hengyang Normal Univ, Coll Math & Stat, Hengyang 421008, Hunan, Peoples R China.
关键词：
Hardy-type space;Bergman-type space;Dirichlet-type space
摘要：
In this paper, we continue our investigation of function spaces on certain classes of complex-valued functions. In particular, we give characterizations on Hardy-type, Bergman-type and Dirichlet-type spaces. Furthermore, we present applications of our results to certain nonlinear PDEs.
期刊：
BULLETIN DES SCIENCES MATHEMATIQUES,2019年154:36-63 ISSN：0007-4497
通讯作者：
Zhu, Jian-Feng
作者机构：
[Chen, Shaolin] Hengyang Normal Univ, Coll Math & Stat, Hengyang 421008, Hunan, Peoples R China.;[Zhu, Jian-Feng] Shantou Univ, Dept Math, Shantou 515063, Guangdong, Peoples R China.;[Zhu, Jian-Feng] Huaqiao Univ, Sch Math Sci, Quanzhou 362021, Fujian, Peoples R China.
通讯机构：
[Zhu, Jian-Feng] S;[Zhu, Jian-Feng] H;Shantou Univ, Dept Math, Shantou 515063, Guangdong, Peoples R China.;Huaqiao Univ, Sch Math Sci, Quanzhou 362021, Fujian, Peoples R China.
关键词：
Schwarz's Lemma;Landau type theorem;Biharmonic equation
摘要：
For g is an element of C((D) over bar), phi is an element of C(T) and f* is an element of C(T), let BH phi,g,f* (D) be the class of all complex-valued functions f is an element of C-4(D) satisfying Delta(Delta f) = g in the unit disk D with Delta f = phi in the unit circle T and f = f* in T, where Delta f is the Laplacian of f. In this article, we will show that several Schwarz type lemmas for f is an element of BH phi,g,f* (D), and, by applying these results, we will establish a Landau type theorem on a subclass of BH phi,g,f* (D). (C) 2019 Elsevier Masson SAS. All rights reserved.
期刊：
Complex Analysis and Operator Theory,2019年13(4):2049-2068 ISSN：1661-8254
通讯作者：
Chen, Shaolin
作者机构：
[Chen, Shaolin] Hengyang Normal Univ, Coll Math & Stat, Hengyang 421008, Hunan, Peoples R China.;[Kalaj, David] Univ Montenegro, Fac Nat Sci & Math, Cetinjski Put B B, Podgorica 81000, Montenegro.
通讯机构：
[Chen, Shaolin] H;Hengyang Normal Univ, Coll Math & Stat, Hengyang 421008, Hunan, Peoples R China.
关键词：
Landau type theorem;Poisson’s equation;Schwarz’s Lemma
摘要：
For a given continuous function
$$g:~\overline{\mathbb {D}}\rightarrow {\mathbb {C}}$$
and a given continuous function
$$\psi :~{\mathbb {T}}\rightarrow {\mathbb {C}}$$
, we establish some Schwarz type Lemmas for mappings f satisfying the PDE:
$$\Delta f=g$$
in
$${\mathbb {D}}$$
, and
$$f=\psi $$
in
$${\mathbb {T}}$$
, where
$${\mathbb {D}}$$
is the unit disk of the complex plane
$${\mathbb {C}}$$
and
$${\mathbb {T}}=\partial {\mathbb {D}}$$
is the unit circle. Then we apply these results to obtain a Landau type theorem, which is a partial answer to the open problem in Chen and Ponnusamy (Bull Aust Math Soc 97: 80–87, 2018).
期刊：
Results in Mathematics,2019年74(3):1-16 ISSN：1422-6383
通讯作者：
Chen, Shaolin
作者机构：
[Chen, Shaolin] Hengyang Normal Univ, Coll Math & Stat, Hengyang 421008, Hunan, Peoples R China.
通讯机构：
[Chen, Shaolin] H;Hengyang Normal Univ, Coll Math & Stat, Hengyang 421008, Hunan, Peoples R China.
关键词：
Length;area;modulus of continuity;Poisson’s equation
摘要：
In this paper, we discuss the modulus of continuity of solutions to Poisson’s equation, and give bounds of length and area distortion for some classes of K-quasiconformal mappings satisfying Poisson’s equations. The obtained results are the extension of the corresponding classical results.
作者机构：
[Chen, Shaolin] Hengyang Normal Univ, Coll Math & Stat, Hengyang 421008, Hunan, Peoples R China.;[Ponnusamy, Saminathan] Indian Inst Technol Madras, Dept Math, Chennai 600036, Tamil Nadu, India.
通讯机构：
[Ponnusamy, Saminathan] I;Indian Inst Technol Madras, Dept Math, Chennai 600036, Tamil Nadu, India.
关键词：
K-quasiconformal harmonic mapping;Radial John disk;Radial length;Pommerenke interior domain
摘要：
In this article, we continue our investigations of the boundary behavior of harmonic mappings. We first discuss the classical problem on the growth of radial length and obtain a sharp growth theorem of the radial length of K-quasiconformal harmonic mappings. Then we present an alternate characterization of radial John disks. In addition, we investigate the linear measure distortion and the Lipschitz continuity on K-quasiconformal harmonic mappings of the unit disk onto a radial John disk. Finally, using Pommerenke interior domains, we characterize certain differential properties of K-quasiconformal harmonic mappings.
作者机构：
[Chen, Shaolin] Hengyang Normal Univ, Coll Math & Stat, Hengyang 421008, Hunan, Peoples R China.;[Ponnusamy, Saminathan] Indian Inst Technol Madras, Dept Math, Chennai 600036, Tamil Nadu, India.
通讯机构：
[Chen, Shaolin] H;Hengyang Normal Univ, Coll Math & Stat, Hengyang 421008, Hunan, Peoples R China.
摘要：
For n >= 3, m >= 1 and a given continuous function g : Omega -> R-m, we establish some Schwarz type lemmas for mappings f of Omega into R-m satisfying the PDE: Delta f = g, where Omega is a subset of R-n. Then we apply these results to obtain a Landau type theorem. (C) 2019 Royal Dutch Mathematical Society (KWG). Published by Elsevier B.V. All rights reserved.
期刊：
BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY,2018年97(1):80-87 ISSN：0004-9727
通讯作者：
Ponnusamy, Saminathan
作者机构：
[Chen, Shaolin] Soochow Univ, Dept Math, Suzhou 215006, Jiangsu, Peoples R China.;[Chen, Shaolin] Hengyang Normal Univ, Coll Math & Stat, Hengyang 421008, Hunan, Peoples R China.;[Ponnusamy, Saminathan] Indian Stat Inst, Chennai Ctr, Stat Math Unit, 110 Nelson Manickam Rd, Madras 600029, Tamil Nadu, India.
通讯机构：
[Ponnusamy, Saminathan] I;Indian Stat Inst, Chennai Ctr, Stat Math Unit, 110 Nelson Manickam Rd, Madras 600029, Tamil Nadu, India.
关键词：
Landau's theorem;(partial derivative)over-bar-equation;Dirichlet-type space
摘要：
<jats:p>The main aim of this article is to establish analogues of Landau’s theorem for solutions to the<jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:type="simple" xlink:href="S0004972717000727_inline2" /><jats:tex-math>$\overline{\unicode[STIX]{x2202}}$</jats:tex-math></jats:alternatives></jats:inline-formula>-equation in Dirichlet-type spaces.</jats:p>
作者机构：
[Chen, Shaolin] Soochow Univ, Dept Math, Suzhou 215006, Jiangsu, Peoples R China.;[Chen, Shaolin] Hengyang Normal Univ, Coll Math & Stat, Hengyang 421008, Hunan, Peoples R China.;[Ponnusamy, Saminathan] ISI, Chennai Ctr, SETS, MGR Knowledge City, CIT Campus, Madras 600113, Tamil Nadu, India.
通讯机构：
[Chen, Shaolin] S;[Chen, Shaolin] H;Soochow Univ, Dept Math, Suzhou 215006, Jiangsu, Peoples R China.;Hengyang Normal Univ, Coll Math & Stat, Hengyang 421008, Hunan, Peoples R China.
