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arXiv · 0706.0756

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

Feng Dai·Yuan Xu
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Abstract

For the weight function $\prod_{i=1}^{d+1}|x_i|^{2\k_i}$ 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.

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Feng Dai, Yuan Xu. 2007-06-06. Boundedness of projection operators and Cesàro means in weighted $L^p$ space on the unit sphere. https://arxiv.org/abs/0706.0756

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