This paper is a summary of the lectures delivered by the author at the Gent Summer School in Analysis and PDE in September 2023. It concerns the boundedness of the generalized spectral projections associated to the sublaplacian in the Heisenberg group, seen as operators from L^1_t L^p_z to L^1_\infty L^q_z. A conjecture about the range of p,q for which the projections are bounded is formulated and some motivations are provided.
Some Norm Bounds for the Spectral Projections of the Heisenberg Sublaplacian
Paolo Ciatti
2024
Abstract
This paper is a summary of the lectures delivered by the author at the Gent Summer School in Analysis and PDE in September 2023. It concerns the boundedness of the generalized spectral projections associated to the sublaplacian in the Heisenberg group, seen as operators from L^1_t L^p_z to L^1_\infty L^q_z. A conjecture about the range of p,q for which the projections are bounded is formulated and some motivations are provided.
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