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Estimates of the maximal Cesaro operators of the weighted orthogonal polynomial expansions in several variables

  • Author / Creator
    Ye, Wenrui
  • Estimates of the maximal Cesaro means at the "critical index'' are established for the orthogonal polynomial expansions (OPEs) with respect to the weight function on the unit sphere. These estimates allow us to improve several known results in this area, including the almost everywhere (a.e.) convergence of the Cesaro means at the "critical index'', the sufficient conditions for the Marcinkiewitcz multiplier theorem, and a Fefferman-Stein type inequality for the Cesaro operators. In addition, several similar results for the weighted OPEs on the unit ball and on the simplex are deduced from the corresponding weighted results on the sphere.

  • Subjects / Keywords
  • Graduation date
    2013-11
  • Type of Item
    Thesis
  • Degree
    Master of Science
  • DOI
    https://doi.org/10.7939/R3MC8RS8J
  • License
    This thesis is made available by the University of Alberta Libraries with permission of the copyright owner solely for non-commercial purposes. This thesis, or any portion thereof, may not otherwise be copied or reproduced without the written consent of the copyright owner, except to the extent permitted by Canadian copyright law.
  • Language
    English
  • Institution
    University of Alberta
  • Degree level
    Master's
  • Department
    • Department of Mathematical and Statistical Sciences
  • Specialization
    • Mathematics
  • Supervisor / co-supervisor and their department(s)
    • Dai, Feng
  • Examining committee members and their departments
    • Safouhi, Hassan (Mathematical and Statistical Sciences)
    • Han, Bin (Mathematical and Statistical Sciences)
    • Lau, Tony (Mathematical and Statistical Sciences)
    • Dai, Feng (Mathematical and Statistical Sciences)