关于齐次群上的奇异积分  

Singular Integrals on Homogeneous Groups

作　　者：孙利民[1] 

机构地区：[1]杭州大学数学系

出　　处：《杭州大学学报（自然科学版）》1992年第4期355-359,共5页Journal of Hangzhou University Natural Science Edition

摘　　要：本文对文[3]中引进的齐次群N(Q)=(R^n×C^m,O)上的奇异积分作了一些讨论.设L(Z)是C^m上的-2m次齐次广义函数,且L(z)∈C~∞(C^m/({0}).令K(t,z)=L(z)6(t),K_s(t,z)=K(t,z)·x(|(t,z)|>e).本文证明了算子Af=f*K及A_,f=f*K_e均可延拓为L^p(N(噩))上的有界算子,1<p<∞.In this paper, we make some discussions about singular integrals on the homogeneous group N(Φ) = (Rn×Cm, ?) introduced in [3] Let L(z) be a distribution on Cm with homogeneous degree-2m, and L(z)∈C∞(Cm\{0}). Let K(t,z)=L(z)·δ(t) and Kε(t,z)=K(t,z)x(|(t,z)| >ε). We prove that Af = f*K and Aε(f) = f*Ke can be extended to bounded operators on Lp(N(Φ)),

关 键 词：齐次群 奇异积分 L^P有界性 

分 类 号：O174[理学—数学]