Fundamental properties of Cauchy--Szeg\H{o} projection on quaternionic Siegel upper half space and applications

We investigate the Cauchy--Szeg\H{o} projection for quaternionic Siegel upper half space to obtain the pointwise (higher order) regularity estimates for Cauchy--Szeg\H{o} kernel and prove that the Cauchy--Szeg\H{o} kernel is non-zero everywhere, which further yields a non-degenerated pointwise lower bound. As applications, we prove the uniform boundedness of Cauchy--Szeg\H{o} projection on every atom on the quaternionic Heisenberg group, which is used to give an atomic decomposition of regular Hardy space $ H^p$ on quaternionic Siegel upper half space for $2/3

Keywords:

• Pointwise
• Kernel (algebra)
• Heisenberg group
• Pure mathematics
• Uniform boundedness
• Siegel upper half-space
• Mathematics
• order
• Hardy space
• Projection (relational algebra)

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