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

  • Maximal Cesaro means
  • Almost everywhere convergence
  • Sphere
  • Simplex
  • Orthogonal polynomial expansions
  • Ball
  • Spherical h-harmonics

• Graduation date

  Fall 2013

• 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.