On a New Integral‐Type Operator from the Weighted Bergman Space tothe Bloch‐Type Space on the Unit Ball | Zendy

Stevo Stević | Zendy

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On a New Integral‐Type Operator from the Weighted Bergman Space tothe Bloch‐Type Space on the Unit Ball

Author(s) -

Stevo Stević

Publication year - 2008

Publication title -

discrete dynamics in nature and society

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.264

H-Index - 39

eISSN - 1607-887X

pISSN - 1026-0226

DOI - 10.1155/2008/154263

Subject(s) - unit sphere , bergman space , type (biology) , mathematics , space (punctuation) , operator (biology) , unit (ring theory) , mathematical analysis , computer science , geology , biology , paleontology , biochemistry , mathematics education , repressor , transcription factor , bounded function , gene , operating system

We introduce an integral-type operator, denoted by Pφg,on the space of holomorphic functions on the unit ball B⊂ℂn, which is an extension of the product of composition andintegral operators on the unit disk. The operator norm ofPφg from the weighted Bergman space Aαp(B) to theBloch-type space ℬμ(B) or the little Bloch-typespace ℬμ,0(B) is calculated. The compactnessof the operator is characterized in terms of inducing functionsg and φ. Upper and lower bounds for the essential normof the operator Pφg:Aαp(B)→ℬμ(B),when p>1, are also given

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