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arXiv · 1703.07859

Bergman-Lorentz spaces on tube domains over symmetric cones

David Bekolle·Jocelyn·Cyrille Nana
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Abstract

We study Bergman-Lorentz spaces on tube domains over symmetric cones, i.e. spaces of holomorphic functions which belong to Lorentz spaces $L(p, q).$ We establish boundedness and surjectivity of Bergman projectors from Lorentz spaces to the corresponding Bergman-Lorentz spaces and real interpolation between Bergman-Lorentz spaces. Finally we ask a question whose positive answer would enlarge the interval of parameters $p\in (1, \infty)$ such that the relevant Bergman projector is bounded on $L^p$ for cones of rank $r\geq 3.$

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David Bekolle, Jocelyn, Cyrille Nana. 2017-03-22. Bergman-Lorentz spaces on tube domains over symmetric cones. https://arxiv.org/abs/1703.07859

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