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Weighted anisotropic integral representations of holomorphic functions in the unit ball of \(\mathbb C^{n}\). (English) Zbl 1225.32008

Author’s abstract: “We obtain integral representations for spaces of functions holomorphic in the unit ball \(B_n\) and belonging to area-integrable weighted \(L^p\)-classes with ‘anisotropic’ weight function of the type \(\prod_{i=1}^n (1-|w_1|^2-|w_2|^2- \dots - |w_i|^2)^{a_i}\), \(w=(w_1, \dots , w_n)\in B_n\). The corresponding kernels of these representations are estimated, written in an integral form, and even written out in an explicit form (for \(n=2\)).”

MSC:

32A26 Integral representations, constructed kernels (e.g., Cauchy, Fantappiè-type kernels)
32A37 Other spaces of holomorphic functions of several complex variables (e.g., bounded mean oscillation (BMOA), vanishing mean oscillation (VMOA))
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References:

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