数学物理学报(英文版)

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BOUNDEDNESS OF RIESZ POTENTIALS IN NONHOMOGENEOUS SPACES

胡国恩; 孟岩; 杨大春   

  1. 北京师范大学数学学院, 北京 100875
  • 收稿日期:2005-12-26 修回日期:2006-06-09 出版日期:2008-04-20 发布日期:2008-04-20
  • 通讯作者: 杨大春
  • 基金资助:

    The research is supported by Program for New Century Excellent Talents
    in University (NCET-04-0142) of China

BOUNDEDNESS OF RIESZ POTENTIALS IN NONHOMOGENEOUS SPACES

Hu Guoen; Meng Yan; Yang Dachun   

  1. School of Mathematical Sciences, Beijing Normal University
    Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing 100875, China
  • Received:2005-12-26 Revised:2006-06-09 Online:2008-04-20 Published:2008-04-20
  • Contact: Yang Dachun

摘要:

For a class of linear operators including Riesz potentials on Rd
with a non-negative Radon measure μ, which only satisfies some growth condition, the authors prove that their boundedness in Lebesgue spaces
is equivalent to their boundedness in the Hardy space or certain weak type endpoint estimates, respectively. As an application, the authors obtain several new end estimates.

关键词: Riesz potential, Lebesgue space, Hardy space, RBMO space, boundedness, non-doubling measure

Abstract:

For a class of linear operators including Riesz potentials on Rd
with a non-negative Radon measure μ, which only satisfies some growth condition, the authors prove that their boundedness in Lebesgue spaces
is equivalent to their boundedness in the Hardy space or certain weak type endpoint estimates, respectively. As an application, the authors obtain several new end estimates.

Key words: Riesz potential, Lebesgue space, Hardy space, RBMO space, boundedness, non-doubling measure

中图分类号: 

  • 47B06