Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

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


Authors: Feng Dai and Yuan Xu
Journal: Trans. Amer. Math. Soc. 361 (2009), 3189-3221
MSC (2000): Primary 33C50, 42B08, 42C10
Published electronically: January 28, 2009
MathSciNet review: 2485423
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 $ 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 [Enhancements On Off] (What's this?)


Similar Articles

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

Retrieve articles in all journals with MSC (2000): 33C50, 42B08, 42C10


Additional Information

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: http://dx.doi.org/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
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
Article copyright: © Copyright 2009 American Mathematical Society