Abstract
In this paper, the Bers-Orlicz spaces on the automorphic formA ϕα (G) (orEA ϕα (G)) andL ϕα (G) on the product Riemann surfaces are studied. We prove that eachf∈A ϕα (G) is a cusp form. Forf∈A ϕα (G), we give the reproducing formula. And, we give the projective operatorP gga fromL ϕα (G) toA ϕα (G) toEA ϕα (G)). After giving some fundamental properties of the Poincaré series, we prove a dual theoremA ϕα (G)=(EA ϕα (G)).
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Supported by the National Nature Science Foundation of China
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Jigang, M., Yuzan, H. Bers-orlicz spaces on the product riemann surface. Acta Mathematica Sinica 10, 249–259 (1994). https://doi.org/10.1007/BF02560716
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DOI: https://doi.org/10.1007/BF02560716