Product Type Operators Involving Radial Derivative Operator Acting between Some Analytic Function Spaces

Manisha Devi, Kuldip Raj and Mohammad Mursaleen
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Manisha Devi: School of Mathematics, Shri Mata Vaishno Devi University, Katra 182320, India
Kuldip Raj: School of Mathematics, Shri Mata Vaishno Devi University, Katra 182320, India
Mohammad Mursaleen: Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan

Mathematics, 2021, vol. 9, issue 19, 1-17

Abstract: Let N denote the set of all positive integers and N 0 = N ∪ { 0 } . For m ∈ N , let B m = { z ∈ C m : | z | < 1 } be the open unit ball in the m − dimensional Euclidean space C m . Let H ( B m ) be the space of all analytic functions on B m . For an analytic self map ξ = ( ξ 1 , ξ 2 , … , ξ m ) on B m and ϕ 1 , ϕ 2 , ϕ 3 ∈ H ( B m ) , we have a product type operator T ϕ 1 , ϕ 2 , ϕ 3 , ξ which is basically a combination of three other operators namely composition operator C ξ , multiplication operator M ϕ and radial derivative operator R . We study the boundedness and compactness of this operator mapping from weighted Bergman–Orlicz space A σ Ψ into weighted type spaces H ω ∞ and H ω , 0 ∞ .

Keywords: weighted Bergman–Orlicz spaces; composition operator; multiplication operator; radial derivative; weighted-type spaces; little weighted type spaces (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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