Transactions of the American Mathematical Society

Boundedness of projection operators and Cesàro means in weighted

space on the unit sphere

Author(s): Feng Dai; Yuan Xu
Journal: Trans. Amer. Math. Soc. 361 (2009), 3189-3221.
MSC (2000): Primary 33C50, 42B08, 42C10
Posted: January 28, 2009
Retrieve article in: PDF

Abstract: For the weight function $\prod_{i=1}^{d+1}\vert x_i\vert^{2\kappa_i}$ 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

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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Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 33C50, 42B08, 42C10

Feng Dai
Affiliation: Department of Mathematical and Statistical Sciences, University of Alberta. Edmonton, Alberta, Canada T6G 2G1
Email: dfeng@math.ualberta.ca

Yuan Xu
Affiliation: Department of Mathematics, University of Oregon, Eugene, Oregon 97403-1222
Email: yuan@math.uoregon.edu

DOI: 10.1090/S0002-9947-09-04846-6
PII: S 0002-9947(09)04846-6
Keywords: Projection operator, Ces\`aro means, weighted $L^p$ space, unit sphere
Received by editor(s): July 19, 2007
Posted: January 28, 2009
Additional Notes: The first author was partially supported by the NSERC Canada under grant G121211001
The second author was partially supported by the NSF under Grant DMS-0604056
Copyright of article: Copyright 2009, American Mathematical Society

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