Maximal function and multiplier theorem for weighted space on the unit sphere |
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| Authors: | Feng Dai Yuan Xu |
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| Affiliation: | a Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta T6G 2G1, Canada
b Department of Mathematics, University of Oregon, Eugene, OR 97403-1222, USA |
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| Abstract: | For a family of weight functions invariant under a finite reflection group, the boundedness of a maximal function on the unit sphere is established and used to prove a multiplier theorem for the orthogonal expansions with respect to the weight function on the unit sphere. Similar results are also established for the weighted space on the unit ball and on the standard simplex. |
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| Keywords: | Maximal function Multiplier h-Harmonics Sphere Orthogonal polynomials Ball Simplex |
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