• 主题
高级搜索  >
历史搜索 清空历史
首页> 外文学位 >MIXED NORM GENERALIZATIONS OF WEIGHTED BERGMAN SPACES IN THE UNIT BALL OF N-DIMENSIONAL COMPLEX SPACE.
【24h】

MIXED NORM GENERALIZATIONS OF WEIGHTED BERGMAN SPACES IN THE UNIT BALL OF N-DIMENSIONAL COMPLEX SPACE.

机译：N维复杂空间单位球中加权Bergman空间的混合范数广义化。

获取原文
获取原文并翻译 | 示例
页面导航
  • 摘要
  • 著录项
  • 相似文献
  • 相关主题

摘要

Let f be an analytic function in the unit ball B of (//C)('N) for which the "mixed norm";is finite. Here 0 < p < (INFIN), 0 < q < (INFIN), (omega) is a suitable radial weight func- tion, and (sigma) is normalized Lebesgue measure on (PAR-DIFF)B. Note that when p = q, because of the "polar coordinates" formula, the space of all such functions is just the Bergman space with weight (omega). General mixed norm spaces were studied extensively by Benedek and Panzone.;We begin by generalizing a collection of results gotten by Luecking for the Bergman spaces or the Hardy spaces. Bounded- ness of certain Bergman projections is proven first, using vector-valued integration and some facts due to Forelli and Rudin. Repre- sentation of the dual space of our mixed norm spaces follows from this. Then a representation of functions in our mixed norm spaces is obtained (by using duality) and several equivalent norms are produced (by refining arguments of Luecking).;We also state a general "Carleson measure theorem" for our mixed norm spaces whose proof depends largely on geometry and the connection between the nonisotropic metric and the invariant Poisson kernel. Several consequences are noted, including a theo- rem originally due to Cima and Wogen. Other related methods and results are given, among them a Carleson measure theorem for mixed norm spaces in the polydisc, a generalization of a result of Hastings.;(DIAGRAM, TABLE OR GRAPHIC OMITTED...PLEASE SEE DAI)
机译：令f为（// C）（'N）的单位球B中的“混合范数”是有限的解析函数。在这里，0 <（INFIN），0

著录项

  • 作者

    GADBOIS, STEVEN CHARLES.;

  • 作者单位

    Michigan State University.;

  • 授予单位 Michigan State University.;
  • 学科 Mathematics.
  • 学位 Ph.D.
  • 年度 1985
  • 页码 48 p.
  • 总页数 48
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

相似文献

  • 外文文献
  • 中文文献
  • 专利
获取原文

客服邮箱：kefu@zhangqiaokeyan.com

京公网安备：11010802029741号 ICP备案号：京ICP备15016152号-6 六维联合信息科技 (北京) 有限公司©版权所有

  • 客服微信

  • 服务号