Extended Cesáro operators from generally weighted Bloch spaces to Zygmund space. (English) Zbl 1170.32003
Summary: Let \(g\) be a holomorphic function of the unit ball \(B\) in the \(n\)-dimensional complex space, and denote by \(T_g\) the extended Cesàro operator with symbol \(g\).
Starting with a brief introduction to well-known results about the Cesàro operator, we investigate the boundedness and compactness of \(T_g\) from generally weighted Bloch spaces \(\mathcal B^{\alpha }_{\log }(0<\alpha <\infty )\) to the Zygmund space \(\mathcal Z\) in the unit ball, and also present some necessary and sufficient conditions.
Starting with a brief introduction to well-known results about the Cesàro operator, we investigate the boundedness and compactness of \(T_g\) from generally weighted Bloch spaces \(\mathcal B^{\alpha }_{\log }(0<\alpha <\infty )\) to the Zygmund space \(\mathcal Z\) in the unit ball, and also present some necessary and sufficient conditions.
MSC:
| 32A37 | Other spaces of holomorphic functions of several complex variables (e.g., bounded mean oscillation (BMOA), vanishing mean oscillation (VMOA)) |
| 32A10 | Holomorphic functions of several complex variables |
Keywords:
Zygmund space; extended Cesàro operators; generally weighted Bloch spaces; boundedness; compactnessReferences:
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