## 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
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**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.## References

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## Additional Information

**Feng Dai**- Affiliation: Department of Mathematical and Statistical Sciences, University of Alberta. Edmonton, Alberta, Canada T6G 2G1
- MR Author ID: 660750
- Email: dfeng@math.ualberta.ca
**Yuan Xu**- Affiliation: Department of Mathematics, University of Oregon, Eugene, Oregon 97403-1222
- MR Author ID: 227532
- Email: yuan@math.uoregon.edu
- Received by editor(s): July 19, 2007
- Published electronically: 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 2009 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**361**(2009), 3189-3221 - MSC (2000): Primary 33C50, 42B08, 42C10
- DOI: https://doi.org/10.1090/S0002-9947-09-04846-6
- MathSciNet review: 2485423