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A Jump Formula of Differential Forms under Berndtsson transform on Complex Manifolds

HUANG Hong yi (Dept. of Comp. Sci., Xiamen Univ.,Xiamen 361005, China)  
By estimating the koppelman kernel on Complex Manifolds, the difference between the koppelman kernel on complex manifolds and the Bochner Martinelli koppelman on C n was obtained;and then by utilizing the koppelman formula and the result as above, the jump formula of differential forms under Berndtsson transform on Complex manifolds was derived. Moreover, by assuming that the Berndtsson transform was continuous on boundary, the plemelj jump was proved. Using the above formulas and selecting suitably complex mainfolds, one can derive some jump formulas including the jump formula on C n and the jump formula on stein manifolds under B M K transform.
【Fund】: 国家自然科学基金!(19771068)
【CateGory Index】: O174.56
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