We prove bounds for the class of Hilbert-type operators associated with generalized powers in a homogeneous cone . Our results extend and slightly improve earlier work from , where the problem was considered for scalar powers and symmetric cones. We give a more transparent proof, provide new examples, and briefly discuss the open question regarding characterization of boundedness for the case of vector indices . Some applications are given to boundedness of Bergman projections in the tube domain over .
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Gustavo Garrigós, Cyrille Nana, Hilbert-type inequalities in homogeneous cones. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 31 (2020), no. 4, pp. 815–838DOI 10.4171/RLM/916