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

Dai, Feng; Xu, Yuan

doi:10.1090/S0002-9947-09-04846-6

Boundedness of projection operators and Cesàro means in weighted $L^p$ space on the unit sphere
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by Feng Dai and Yuan Xu PDF

Trans. Amer. Math. Soc. 361 (2009), 3189-3221 Request permission

Abstract:

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

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