Authors: Chang, Der Chen
Li, Songxiao
Stević, Stevo 
Affiliations: Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: On some integral operators on the unit polydisk and the unit ball
Journal: Taiwanese Journal of Mathematics
Volume: 11
Issue: 5
First page: 1251
Last page: 1285
Issue Date: 1-Jan-2007
Rank: M23
ISSN: 1027-5487
DOI: 10.11650/twjm/1500404862
Let Dn be the unit polydisk and B be the unit ball in Cn respectively. In this paper, we extend the Cesàro operator to the unit polydisk and the unit ball. We prove that the generalized Cesàro operator, is bounded on the Hardy space Hp(Dn) and the mixed norm space, when 0 < q < ∞, p ∈ (0,1] and Re(bj +1) > Recj > 0, j = 1,...,n, or if 0 < q < ∞, p>1 and Re(bj+1) > Re cj ≥ 1, j=1,...,n. Here, and each μj, j ∈ {1,..., n} is a positive Borel measure on the interval [0, 1). We also introduce a new class of averaging integral operators Cb,cζ0 (the generalized Cesàro operators) on B and prove the boundedness of the operator on the Hardy space Hp(B), p ∈ (0, ∞), the mixed-norm space Ap,qμ(B), 0 < p, q < ∞ and the α-Bloch space, when α > 1. Finally, we study the boundedness and compactness of recently introduced Riemann-Stieltjes type operators Tg and Lg, from H∞ and Bergman type spaces to α-Bloch spaces and little α-Bloch spaces on B.
Keywords: Bergman space | Bloch space | Boundedness | Cesàro operator | Compactness | Hardy space | Riemann-Stieltjes operator
Publisher: Mathematical Society of the Republic of China
Project: NNSF China (No.10671115)
PhD Foundation (No.20060560002)
NSF of Guangdong Province (No. 06105648)

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