Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 44, 2019, 427-448

CHARACTERIZATIONS OF HARDY-TYPE, BERGMAN-TYPE AND DIRICHLET-TYPE SPACES ON CERTAIN CLASSES OF COMPLEX-VALUED FUNCTIONS

Shaolin Chen, Antti Rasila and Matti Vuorinen

Hengyang Normal University, College of Mathematics and Statistics
Hengyang, Hunan 421008, P.R. China; mathechen 'at' 126.com

Guangdong Technion – Israel Institute of Technology, College of Science
241 Daxue Road, Shantou, Guangdong 515063, P.R. China; antti.rasila 'at' gtiit.edu.cn

University of Turku, Department of Mathematics and Statistics
Turku 20014, Finland; vuorinen 'at' utu.fi

Abstract. 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.

2010 Mathematics Subject Classification: Primary 32A10, 30D55; Secondary 30C65, 58J10.

Key words: Hardy-type space, Bergman-type space, Dirichlet-type space.

Reference to this article: S. Chen, A. Rasila and M. Vuorinen: Characterizations of Hardy-type, Bergman-type and Dirichlet-type spaces on certain classes of complex-valued functions. Ann. Acad. Sci. Fenn. Math. 44 (2019), 427-448.

Full document as PDF file

https://doi.org/10.5186/aasfm.2019.4426