Bochner-Martinelli型积分的边界性质

Boundary properties of Bochner-Martinelli type integral

对 Cn中具光滑边界Ω的有界域 D和属于指数α( 0 <α <1 )的 Lipschitz空间 Lip(α,Ω )中的每个函数φ,我们不仅证明了 Bochner- Martinelli型积分Φ ( z) =∫Ωφ(ζ) K(ζ,z)(其中 K(ζ,z)为 Bochner- Martinelli型积分核 )表示的内、外极限值Φ +( t) ,Φ - ( t)属于 Lip(β,Ω ) ( 0 <β <α <1 )而且可分别延拓成 D和 Dc上的指数为β的 Holder连续函数 ,并由此给出了 Bochner- Martinelli变换的 Plemelj跳跃公式 .

This paper, one shows that the inner and outer limit val ues Φ+(t) and Φ-(t) of Φ(z) for the erpresentation of Bochner-Martinelli type integral are belong to Lip) and which limits can be extended to Holder continuous functions with exponent β in D and Dc, respectively, for each function φ belongs to Lip(α,Ω) with exponent α,DC n a boun ded domain with smooth boundary Ω, and by using these facts give the jump formula for the Bochner-Martinelli transformation.