Fundamental properties of Cauchy--Szegő projection on quaternionic Siegel upper half space and applications

2021/10/23 by Der‐Chen Chang, Chang, Der-Chen, Xuan Thinh Duong +7
Mathematics · #Algebraic and Geometric Analysis #Mathematical Analysis and Transform Methods #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.2110.12210

Abstract

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^p on quaternionic Siegel upper half space for 2/3

Citations

• Nearly weakly orthonormal sequences, singular value estimates, and Calderon-Zygmund operators

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