Multipliers for logarithmic Cauchy integrals in the ball. (English. Russian original) Zbl 1288.32009
J. Math. Sci., New York 166, No. 1, 23-30 (2010); translation from Zap. Nauchn. Semin. POMI 370, 44-57 (2009).
Summary: Let \(B_n\) denote the unit ball in \(\mathbb C^n\), \(n\geq 1\). Let \(\mathcal{K}_0(n)\) denote the class of functions defined for \(z\in B_n\) as a constant plus the integral of the kernel \(\log(1/(1-\langle z,\zeta\rangle ))\) against a complex Borel measure on the sphere \(\{\zeta\in\mathbb C^n:| \zeta| =1\}\). Properties of holomorphic functions \(g\) such that \(fg\in\mathcal{K}_0(n)\) for all \(f\in\mathcal{K}_0(n)\) are studied. The extended Cesàro operators are investigated on the spaces \(\mathcal{K}_0(n)\), \(n\geq 1\).
MSC:
| 32A37 | Other spaces of holomorphic functions of several complex variables (e.g., bounded mean oscillation (BMOA), vanishing mean oscillation (VMOA)) |
| 32M15 | Hermitian symmetric spaces, bounded symmetric domains, Jordan algebras (complex-analytic aspects) |
| 46E15 | Banach spaces of continuous, differentiable or analytic functions |
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