Boundedness of projection operators and Cesàro means in weighted L^p space on the unit sphere

2007/06/06 by Chang‐Feng Dai, Yuan Xu, Dai, Feng +1
Mathematics · #33C50 #42B08 #42C10 #Advanced Harmonic Analysis Research #Approximation Theory and Sequence Spaces #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical functions and polynomials

paper · pdf · doi:10.48550/arxiv.0706.0756

openalex publication_date 2007/06/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For the weight function ∏_i=1^d+1|x_i|^2\k_i on the unit sphere, sharp local estimates of the orthogonal projection operators are obtained and used to prove the convergence of the Cesàro (C,δ) means in the weighted L^p space for δ below the critical index. Similar results are also proved for corresponding weight functions on the unit ball and on the simplex.

Citations

• Mean convergence of orthogonal series
• Differential-difference operators associated to reflection groups
• Cesàro means of orthogonal expansions in several variables

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• Almost everywhere convergence of orthogonal expansions of several variables
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