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- Title
- Spherical maximal functions on two step nilpotent Lie groups
- KIAS Author
- Ryu, Jaehyeon,Ryu, Jaehyeon
- Journal
- ADVANCES IN MATHEMATICS, 2024
- Archive
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- Abstract
- Consider R d x R m with the group structure of a twostep nilpotent Lie group and natural parabolic dilations. The maximal function originally introduced by Nevo and Thangavelu in the setting of the Heisenberg group deals with noncommutative convolutions associated to measures on spheres or generalized spheres in R d . We drop the nondegeneracy assumptions in the known results on M & eacute;tivier groups and prove the sharp L p boundedness result for all two step nilpotent Lie groups with d >= 3. (c) 2024 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.