Bulletin of Pure & Applied Sciences- Mathematics and Statistics
  • Year: 2020
  • Volume: 39e
  • Issue: 2

A new product of superposition and differentiation operators between Hardy and Zygmund spaces*

  • Author:
  • A. Kamal1, M. Hamza Eissa2, Lalit Mohan Upadhyaya3, Ayman Shehata4
  • Total Page Count: 13
  • Published Online: Aug 30, 2021
  • Page Number: 193 to 205

1. Department of Mathematics, College of Science and Arts at Muthnib, Qassim University, Qassim, Kingdom of Saudi Arabia.

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

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

4. Department of Mathematics, College of Science and Arts at Unaizah, Qassim University, Qassim, Kingdom of Saudi Arabia., Department of Mathematics, Faculty of Science, Assiut University, Assiut71516, Egypt.

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

2. E-mail: mohammed_essa2001@yahoo.com

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

4. E-mail: drshehata2006@yahoo.com

Abstract

Our goal in this article is to characterize the boundedness and the compactness of the product of the superposition operator followed by the differentiation operator DSϕ from the H∞ space to the Zygmund space. Moreover, we give the necessary and sufficient conditions for the DSϕ operator from the H∞ space to the Zygmund space to be bounded and compact.

Keywords

Superposition operator, Differentiation operator, Compactness, DSϕ operator