Volterra Type Operators on Weighted Dirichlet*

Citation:

Qingze LIN.Volterra Type Operators on Weighted Dirichlet*[J].Chinese Annals of Mathematics B,2021,42(4):601~612
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Authors:

Qingze LIN;

Foundation:

National Natural Science Foundation of China (No. 11801094).
Abstract: The Carleson measures for weighted Dirichlet spaces had been characterized by Girela and Pel′aez, who also characterized the boundedness of Volterra type operators between weighted Dirichlet spaces. However, their characterizations for the boundedness are not complete. In this paper, the author completely characterizes the boundedness and compactness of Volterra type operators from the weighted Dirichlet spaces Dpα to Dqβ (?1 < α, β and 0 < p < q < ∞), which essentially complete their works. Furthermore, the author investigates the order boundedness of Volterra type operators between weighted Dirichlet spaces.

Keywords:

Volterra type operator, Boundedness, Compactness, Weighted Dirichlet space, Order boundedness

Classification:

47G10, 31C25, 47B38
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