Bulletin of Pure and Applied Sciences Section - E - Mathematics & Statistics
  • Year: 2020
  • Volume: 39e
  • Issue: 1

Boundedness of composition operators on some analytic function spaces *

  • Author:
  • A. Kamal1,†, S.A. El-Hafeez2,, Lalit Mohan Upadhyaya3,, Ayman Shehata4,
  • Total Page Count: 12
  • Published Online: Jun 1, 2020
  • Page Number: 46 to 57

1Department of Mathematics, College of Science and Arts in Muthnib, Qassim University, Qassim, Kingdom of Saudi Arabia. Department of Mathematics, Faculty of Science, Port Said University, Port Said, Egypt

2Department of Mathematics, Faculty of Science, Port Said University, Port Said, Egypt

3Department of Mathematics, Municipal Post Graduate College, Mussoorie, Dehradun, Uttarakhand-248179, India

4Department of Mathematics, Faculty of Science, Assiut University, Assiut, 71516, Egypt. Department of Mathematics, College of Science and Arts, Unaizah, Qassim University, Qassim, Kingdom of Saudi Arabia

†Corresponding author A. Kamal, E-mail: alaa_mohamed1@yahoo.com

*E-mail: samyabdelhafeez@yahoo.com

**E-mail: lmupadhyaya@rediffmail.com, hetchres@gmail.com

***E-mail: drshehata2006@yahoo.com

Online published on 14 August, 2020.

Abstract

In this paper, we investigate the necessary and sufficient conditions for a composition operator Cϕ to be bounded and compact from to QK,ω(p, q). Moreover, the necessary and sufficient condition for Cϕ from the Dirichlet space 𝒟 to the space QK,ω(p, q) to be compact is also given in terms of the map ϕ.

Keywords

QK,ω(p, q) spaces, holomorphic functions and weighted α-Bloch space, Primary, 47B33, Secondary, 46E15