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arXiv · 0705.2477

Cesàro means of orthogonal expansions in several variables

Feng Dai·Yuan Xu
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Abstract

Cesàro $(C,δ)$ means are studied for orthogonal expansions with respect to the weight function $\prod_{i=1}^{d}|x_i|^{2\k_i}$ on the unit sphere, and for the corresponding weight functions on the unit ball and the Jacobi weight on the simplex. A sharp pointwise estimate is established for the $(C,\d)$ kernel with $\d > -1$ and for the kernel of the projection operator, which allows us to derive the exact order for the norm of the Cesàro means and the projection operator on these domains.

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Feng Dai, Yuan Xu. 2007-05-17. Cesàro means of orthogonal expansions in several variables. https://arxiv.org/abs/0705.2477

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