Analysis of the Sublaplacian
In this chapter we study the spectral theory of the sublaplacian as developed by Strichartz. We obtain an Abel summability result for expansions in terms of the eigenfunctions of the sublaplacian. For the spectral projection operators, we establish some restriction theorems. Using the restriction theorem, we study the Bochner-Riesz means for the sublaplacian. We also develop a Littlewood-Paley-Stein theory for the sublaplacian and prove a multiplier theorem for the Fourier transform.
KeywordsRestriction Theorem Heisenberg Group Spectral Projection Multiplier Theorem Laguerre Function
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