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This chapter concerns the boundedness of the generalized spectral projections \(\mathcal P_\lambda \) associated to the sublaplacian in the Heisenberg group, seen as operators from \(L^1_t L^p_{z}\) to \(L^\infty _t L^q_{z}\) . We formulate a conjecture about the range of \(p,q\) for which the projections \(\mathcal P_\lambda \) are bounded and provide some motivations.

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Some Mixed Norm Bounds for the Spectral Projections of the Heisenberg Sublaplacian

  • 章节

  • 发表日期：

    2025年

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  • Valentina Casarino,
  • Paolo Ciatti

摘要

This chapter concerns the boundedness of the generalized spectral projections \(\mathcal P_\lambda \) associated to the sublaplacian in the Heisenberg group, seen as operators from \(L^1_t L^p_{z}\) to \(L^\infty _t L^q_{z}\) . We formulate a conjecture about the range of \(p,q\) for which the projections \(\mathcal P_\lambda \) are bounded and provide some motivations.