Maximal estimates for the Ces¨¤ro means of weighted orthogonal polynomial expansions on the unit sphere

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• 作者：Feng Dai ; Sheng Wang ; Wenrui Ye
• 关键词：Spherical h-harmonics ; Maximal Cesà ; ro means ; Almost everywhere convergence ; Sphere ; Orthogonal polynomial expansions ; Ball ; Simplex
• 刊名：Journal of Functional Analysis
• 出版年：2013
• 出版时间：15 November, 2013
• 年：2013
• 卷：265
• 期：10
• 页码：2357-2387
• 全文大小：328 K

文摘

Estimates of the maximal Ces¨¤ro means at the ¡°critical index¡± are established for the orthogonal polynomial expansions (OPEs) with respect to the weight function on the unit sphere of . These estimates allow us to improve several known results in this area, including the almost everywhere (a.e.) convergence of the Ces¨¤ro means at the ¡°critical index¡±, the sufficient conditions for the Marcinkiewitcz multiplier theorem, and a Fefferman-Stein type inequality for the Ces¨¤ro 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.