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Volterra integral operators on a family of Dirichlet-Morrey spaces

Hu Lian, Liu Xiaosong

Opuscula Mathematica

2023

Vol. 43, no. 5

633--649

A family of Dirichlet-Morrey spaces Dλ,K of functions analytic in the open unit disk D are defined in this paper. We completely characterize the boundedness of the Volterra integral operators Tg, Ig and the multiplication operator Mg on the space Dλ,K. In addition, the compactness and essential norm of the operators Tg and Ig on Dλ,K are also investigated.

Weighted composition operators via Berezin transform and Carleson measure

Kumar R., Singh K. J.

Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae

2006

Vol. 46, [Z] 1

63-78

In this paper, we study the boundedness and the compactness of weighted composition operators on Hardy spaces and weighted Bergman spaces of the unit polydisc in C^n.