Abstract
We use a family of atomic decomposition operators to determine an explicit function realising the complex interpolation between two mixed norm weighted Bergman spaces in tube domains over open convex homogneous cones. Our results extend and improve earlier work from (Békollé et al. in C R Acad Sci Paris Ser I(337):13–18, 2003), where the problem was considered for scalar powers \({\varvec{{\alpha }}}=({\alpha },\ldots ,{\alpha })\) and symmetric cones \(\Omega \).
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Acknowledgements
The authors express their gratitude to Professor Gustavo Garrigós and Professor David Békollé for fruitful discussions on the topic. The second author thanks the University of Murcia and the Erasmus Plus Program for their hospitality and support during a research visit in which part of this work was carried out. The authors also express their gratitude to the referee for the thorough review of the manuscript and the suggestion of some key references needed to improve the quality of the work.
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Communicated by H. Turgay Kaptanoglu.
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This article is part of the topical collection“Harmonic Analysis and Operator Theory” edited by H. Turgay Kaptanoglu, Andreas Seeger, Franz Luef and Serap Oztop.
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Gonessa, J., Mbapte, R.F. & Nana, C. Complex Interpolation Between Two Mixed Norm Bergman Spaces in Tube Domains Over Homogeneous Cones. Complex Anal. Oper. Theory 17, 56 (2023). https://doi.org/10.1007/s11785-023-01365-5
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DOI: https://doi.org/10.1007/s11785-023-01365-5