کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4618482 1339407 2011 11 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
On inner functions with HpHp and BpBp derivatives in the unit ball of CnCn
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات آنالیز ریاضی
پیش نمایش صفحه اول مقاله
On inner functions with HpHp and BpBp derivatives in the unit ball of CnCn
چکیده انگلیسی

Let BnBn be the unit ball in CnCn. If f is a bounded holomorphic function, we say that f is inner provided thatlimr→1−|f(rζ)|=1σ-a.e.,ζ∈Sn where SnSn is the unit sphere and σ   is normalized surface measure on SnSn. If β>−1β>−1 and p>0p>0 then Aβp denotes the weighted Bergman space of all holomorphic functions weighted by β(1−|z|2)(1−|z|2)β. For 00p>0 let HpHp denote the usual Hardy space of holomorphic functions on the ball. In this paper, we consider derivatives of inner functions in several spaces of holomorphic functions. If f   is an inner function, membership of the radial derivative, Rf=∑j=1nzj∂f∂zj, will be considered in the BpBp spaces for p>nn+1 and will be related to membership in weighted Dirichlet spaces, weighted Bergman spaces Aα2 for 0<α<10<α<1, and to the ApAp spaces for 11n>1, and either Rf∈B2n2n+1, Rf∈A3/2Rf∈A3/2, or Rf∈H1/2Rf∈H1/2 then f must be constant.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Mathematical Analysis and Applications - Volume 378, Issue 1, 1 June 2011, Pages 295–305
نویسندگان
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