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

A Kamal; M Hamza Eissa; Lalit Mohan Upadhyaya; Ayman  Shehata

doi:10.48165/

Authors

A Kamal Department of Mathematics, College of Science and Arts at Muthnib, Qassim University, Qassim, Kingdom of Saudi Arabia.
M Hamza Eissa Department of Mathematics, Faculty of Science, Port Said University, Port Said, Egypt
Lalit Mohan Upadhyaya Department of Mathematics, Municipal Post Graduate College, Mussoorie, Dehradun, Uttarakhand-248179, India.
Ayman Shehata Department of Mathematics, Faculty of Science, Assiut University, Assiut 71516, Egypt.

DOI:

https://doi.org/10.48165/

Keywords:

Superposition operatoR, differentiation operator, compactness, DSϕ oper ator

Abstract

Our goal in this article is to characterize the boundedness and the compact ness 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.

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