Maximal function and Multiplier Theorem for Weighted Space on the Unit Sphere

Details Maximal function and Multiplier Theorem for Weighted Space on the Unit Sphere Maximal function and Multiplier Theorem for Weighted Space on the Unit Sphere

2007-03-30

arxiv.org/abs/math/0703928v1

Mathematics

Classical Analysis and ODEs

24 pages, to appear in J. Funct. Analysis

Scientific paper

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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