首页 | 本学科首页   官方微博 | 高级检索  
     


A Class of Integral Operators on the Unit Ball ofmathbb{C}^{n}
Authors:Osman Kures  Kehe Zhu
Affiliation:(1) Department of Mathematics, State University of New York, Albany, NY 12222, USA
Abstract:For real parameters a, b, c, and t, where c is not a nonpositive integer, we determine exactly when the integral operator
$$ Tf(z) = {left( {1 - |z|^{2} } right)}^{a} {int_{mathbb{B}_{n} } {frac{{{left( {1 - |w|^{2} } right)}^{b} }} {{{left( {1 - langle z,wrangle } right)}^{c} }}f(w);dv(w)} } $$
is bounded on $$L^{p} {left( {mathbb{B}_{n} ,;dv_{t} } right)},$$ where $$mathbb{B}_{n}$$ is the open unit ball in $$mathbb{C}^{n} ,;1 leq p < infty ,$$ and dvt (z)  =  (1  −  |z| 2) t dv (z) with dv being volume measure on $$mathbb{B}_{n} .$$ The characterization remains the same if we replace (1  −  〈zw 〉) c in the integral kernel above by its modulus |1  −  〈zw〉| c.
Keywords:  KeywordHeading"  >Mathematics Subject Classification (2000). 47G10
本文献已被 SpringerLink 等数据库收录!
设为首页 | 免责声明 | 关于勤云 | 加入收藏

Copyright©北京勤云科技发展有限公司  京ICP备09084417号