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Bulletin of Pure and Applied Sciences- Math& Stat. (Started in 1982)
eISSN: 2320-3226
pISSN: 0970-6577
Impact Factor: 4.895 (2017)
DOI: 10.5958/2320-3226
Editor-in-Chief:  Prof. Dr. Lalit Mohan Upadhyaya
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Article Details

Bulletin of Pure and Applied Sciences- Math& Stat. (Started in 1982)
Year : 2020, Volume & Issue : BPAS-Maths & Stat 39E(1), JAN-JUN 2020
Page No. : 46-57, Article Type : Original Aticle
Article DOI : 10.5958/2320-3226.2020.00004.1 (Communicated, edited and typeset in Latex by Jyotindra C. Prajapati (Editor). Received May 04, 2019 / Revised March 28, 2020 / Accepted April 23, 2020. Online First Published on June 30, 2020)

Boundedness of composition operators on some analytic function spaces

A. Kamal1, S.A. El-Hafeez2, Lalit Mohan Upadhyaya3 and Ayman Shehata4
Author’s Affiliation : 1. Department of Mathematics, College of Science and Arts in Muthnib, Qassim University, Qassim, Kingdom of Saudi Arabia. 1,2. 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, Faculty of Science, Assiut University, Assiut 71516, Egypt. 4. Department of Mathematics, College of Science and Arts, Unaizah, Qassim University, Qassim, Kingdom of Saudi Arabia. 1. E-mail: [email protected] , 2. E-mail: [email protected] 3. E-mail: [email protected] , [email protected] 4. E-mail: [email protected]

Corresponding Author : A. Kamal,
E-Mail:-[email protected]


Abstract

In this paper, we investigate the necessary and sufficient conditions  for a composition operator $C_phi$ to be bounded and compact from ${cal B}_{omega}^{alpha}$ to $Q_{K,omega}(p,q)$. Moreover, the necessary and sufficient condition for $C_{phi}$ from the Dirichlet space $mathcal{D}$ to the space $Q_{K, omega}(p,q)$ to be compact is also given in terms of the map $phi$.

Keywords

$Q_{K,omega}(p, q)$ spaces, holomorphic functions and weighted $alpha$-Bloch space. 2020 Mathematics Subject Classification: Primary: 47B33; Secondary: 46E15.
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