Hankel and Berezin Type Operators on Weighted Besov Spaces of Holomorphic Functions on Polydisks |
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Authors: | A V Harutyunyan G Marinescu |
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Institution: | 1.Yerevan State University,Yerevan,Armenia;2.University of Cologne,Cologne,Germany |
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Abstract: | Let S be the space of functions of regular variation and let ω = (ω1,..., ωn), ωj ∈ S. The weighted Besov space of holomorphic functions on polydisks, denoted by B p (ω) (0 < p < +∞), is defined to be the class of all holomorphic functions f defined on the polydisk U n such that \(||f||_{{B_{P(\omega )}}}^P = \int_{{U^n}} {|Df(z){|^p}\prod\limits_{j = 1}^n {{\omega _j}{{(1 - |{z_j}{|^2})}^{P - 2}}dm{a_{2n}}(z) < \infty } } \), where dm2n(z) is the 2ndimensional Lebesgue measure on U n and D stands for a special fractional derivative of f.We prove some theorems concerning boundedness of the generalized little Hankel and Berezin type operators on the spaces B p (ω) and L p (ω) (the weighted L p -space). |
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