On some class of integral operators related to the Bergman projection | Zendy

Djordjije Vujadinović | Zendy

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On some class of integral operators related to the Bergman projection

Author(s) -

Djordjije Vujadinović

Publication year - 2015

Publication title -

publications de l institut mathematique

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.246

H-Index - 17

eISSN - 1820-7405

pISSN - 0350-1302

DOI - 10.2298/pim150220023v

Subject(s) - mathematics , bergman space , hilbert space , invariant (physics) , projection (relational algebra) , measure (data warehouse) , pure mathematics , space (punctuation) , unit disk , complex plane , mathematical analysis , combinatorics , mathematical physics , bounded function , algorithm , computer science , linguistics , philosophy , database

We consider the integral operator C?f(z) = ?D f(?)/(1-z?)? dA(?), z ? D, where 0 < ? < 2 and D is the unit disc in the complex plane. and investigate boundedness of it on the space Lp(D, d?), 1 < p < 1, where d? is the M?bius invariant measure in D. We also consider the spectral properties of C? when it acts on the Hilbert space L2(D, d?), i.e., in the case p = 2, when C? maps L2(D, d?) into the Dirichlet space.

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