Geodesic
A class of Hausdorff–Berezin operators on the unit ball
Canadian mathematical bulletin, Tome 67 (2024) no. 4, pp. 1069-1080

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DOI

The article introduces and studies Hausdorff–Berezin operators on the unit ball in a complex space. These operators are a natural generalization of the Berezin transform. In addition, the class of such operators contains, for example, the invariant Green potential, and some other operators of complex analysis. Sufficient and necessary conditions for boundedness in the space of p – integrable functions with Haar measure (invariant with respect to involutive automorphisms of the unit ball) are given. We also provide results on compactness of Hausdorff–Berezin operators in Lebesgue spaces on the unit ball. Such operators have previously been introduced and studied in the context of the unit disc in the complex plane. Present work is a natural continuation of these studies.
DOI : 10.4153/S000843952400050X
Mots-clés : Hausdorff operators, Berezin transform, Haar measure, Möbius group 
Karapetyants, Alexey; Mirotin, Adolf. A class of Hausdorff–Berezin operators on the unit ball. Canadian mathematical bulletin, Tome 67 (2024) no. 4, pp. 1069-1080. doi: 10.4153/S000843952400050X
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     title = {A class of {Hausdorff{\textendash}Berezin} operators on the unit ball},
     journal = {Canadian mathematical bulletin},
     pages = {1069--1080},
     year = {2024},
     volume = {67},
     number = {4},
     doi = {10.4153/S000843952400050X},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/S000843952400050X/}
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