On some integral operators on the unit polydisk and the unit ball. (English) Zbl 1149.47026

Chang, Der-Chen; Li, Songxiao; Stević, Stevo

Taiwanese J. Math. 11, No. 5, 1251-1285 (2007).

The authors prove boundedness theorems for some generalized Cesàro operators on various spaces of holomorphic functions in the unit polydisk or ball \(\mathbb B_n\) in \(\mathbb C^n\). Boundedness and compactness of some Riemann-Stieltjes type operators from \(H^\infty\) and Bergman spaces to \(\alpha\)-Bloch spaces on \(\mathbb B_n\) are investigated, too. The paper contains a wealth of material and a useful reference list of 51 items.

Reviewer: Raymond Mortini (Metz)

MSC:

47B38	Linear operators on function spaces (general)
46E15	Banach spaces of continuous, differentiable or analytic functions
47G10	Integral operators

Keywords:

Cesàro operator; Riemann-Stieltjes operator; Hardy spaces; Bergman spaces; boundedness; compactness