• Corpus ID: 239769117

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

  title={Fundamental properties of Cauchy--Szeg\H\{o\} projection on quaternionic Siegel upper half space and applications},
  author={Der-Chen Chang and Xuan Thinh Duong and Ji Li and Wei Wang and Qingyan Wu},
We investigate the Cauchy–Szegő projection for quaternionic Siegel upper half space to obtain the pointwise (higher order) regularity estimates for Cauchy–Szegő kernel and prove that the Cauchy– Szegő kernel is non-zero everywhere, which further yields a non-degenerated pointwise lower bound. As applications, we prove the uniform boundedness of Cauchy–Szegő projection on every atom on the quaternionic Heisenberg group, which is used to give an atomic decomposition of regular Hardy space H on… 


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