C^n中的分数次Cauchy-Stieltjes积分族  

FAMILIES OF FRACTIONAL CAUCHY-STIELTJES INTEGRALS IN C_n

作　　者：刘聪文[1] 史济怀[1] 

机构地区：[1]中国科学技术大学数学系,合肥230026

出　　处：《数学年刊（A辑）》2002年第3期297-306,共10页Chinese Annals of Mathematics

基　　金：国家自然科学基金(No.19871081);中国科学院特支费资助的项目.

摘　　要：本文研究多复变数的分数次Cauchy-Stieltjes积分组成的函数族Fp,p≥0,这里函数族Fp（p>0）和F0分别由形如f（z）=∫S1/（1<z,ζ>）pdμ（ζ）和f（z）=∫Slog1/1-<z,ζ>dμ（ζ）的全纯函数f组成,其中μ是Cn中单位球S上的复Borel测度.本文考察了Fp的一些有趣的性质,并研究了它与Hardy空间,Dirichlet型空间和BMOA等的关系.The authors consider the families Fp,p≥ 0, of fractional Cauchy-Stieltjes integrals in several variables. The families Fp(p > 0) and F0 consist of all functions f of the formsf(z) =∫s 1/(1-<z,ζ>)pdμ(ζ) and f(z) = ∫slog1/1-<z,ζ>dμ(ζ)respectively, where μ is a complex Borel measure on the unit sphere S. Various interesting properties of Fp are investigated and the relations between Fp and other function spaces such as Hardy classes, BMOA and Dirichlet type spaces are also studied in this paper.

关 键 词：分数次Cauchy-Stieltjes积分 Mobius不变族 HARDY空间 BMOA 

分 类 号：O174.56[理学—数学]