A new technique of integral representations in ℂ n
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A new technique of integral representations in ℂ n , which is different from the well-known Henkin technique, is given. By means of this new technique, a new integral formula for smooth functions and a new integral representation of solutions of the ∂-equations on strictly pseudoconvex domains in ℂ n are obtained. These new formulas are simpler than the classical ones, especially the solutions of the ∂-equations admit simple uniform estimates. Moreover, this new technique can be further applied to arbitrary bounded domains in ℂ n so that all corresponding formulas are simplified.
Keywordsstrictly pseudoconvex domain smooth function integral representation ∂-equation new technique
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