数学物理学报(英文版) ›› 2012, Vol. 32 ›› Issue (3): 907-928.doi: 10.1016/S0252-9602(12)60069-1

• 论文 • 上一篇    下一篇

OSCILLATION AND VARIATION OF THE LAGUERRE HEAT AND POISSON SEMIGROUPS AND RIESZ TRANSFORMS

J.J. Betancor, R. Crescimbeni, J.L. Torrea   

  1. 1.Departamento de An´aisis Matem´aico, Universidad de La Laguna, 38271-La Laguna, Tenerife, Islas Canarias, Spain|2.Departamento de Matem´aica, Universidad Nacional del Comahue, Buenos Aires 1400, 8300 Neuqu´en, Argentina|3.Departamento de Matem´aticas, Facultad de Ciencias, Universidad Aut´onoma de Madrid, 28049 Madrid, Spain
  • 收稿日期:2010-03-03 修回日期:2011-01-28 出版日期:2012-05-20 发布日期:2012-05-20
  • 基金资助:

    The first author is partially supported by Ministerio de Educaci´on y Ciencia (Spain), grant MTM2007-65609. The second author is partially supported by Universidad Nacional del Comahue (Argentina) and Ministerio de Educaci´on y Ciencia (Spain) grant PCI 2006-A7-0670. The
    third author is partially supported by Ministerio de Educaci´on y Ciencia (Spain), grant MTM 2008-06621-C02.

OSCILLATION AND VARIATION OF THE LAGUERRE HEAT AND POISSON SEMIGROUPS AND RIESZ TRANSFORMS

J.J. Betancor, R. Crescimbeni, J.L. Torrea   

  1. 1.Departamento de An´aisis Matem´aico, Universidad de La Laguna, 38271-La Laguna, Tenerife, Islas Canarias, Spain|2.Departamento de Matem´aica, Universidad Nacional del Comahue, Buenos Aires 1400, 8300 Neuqu´en, Argentina|3.Departamento de Matem´aticas, Facultad de Ciencias, Universidad Aut´onoma de Madrid, 28049 Madrid, Spain
  • Received:2010-03-03 Revised:2011-01-28 Online:2012-05-20 Published:2012-05-20
  • Supported by:

    The first author is partially supported by Ministerio de Educaci´on y Ciencia (Spain), grant MTM2007-65609. The second author is partially supported by Universidad Nacional del Comahue (Argentina) and Ministerio de Educaci´on y Ciencia (Spain) grant PCI 2006-A7-0670. The
    third author is partially supported by Ministerio de Educaci´on y Ciencia (Spain), grant MTM 2008-06621-C02.

摘要:

In this article, we study Lp-boundedness properties of the oscillation and vari-ation operators for the heat and Poissson semigroup and Riesz transforms in the Laguerre settings. Also, we characterize Hardy spaces associated to Laguerre operators by using the
variation operator of the heat semigroup.

关键词: Oscillation, variation, heat Laguerre semigroup, Riesz transforms

Abstract:

In this article, we study Lp-boundedness properties of the oscillation and vari-ation operators for the heat and Poissson semigroup and Riesz transforms in the Laguerre settings. Also, we characterize Hardy spaces associated to Laguerre operators by using the
variation operator of the heat semigroup.

Key words: Oscillation, variation, heat Laguerre semigroup, Riesz transforms

中图分类号: 

  • 42A50