Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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SZEGÖ PROJECTIONS FOR HARDY SPACES IN QUATERNIONIC CLIFFORD ANALYSIS

  • He, Fuli (School of Mathematics and Statistics, HNP-LAMA Central South University) ;
  • Huang, Song (School of Mathematics and Statistics, HNP-LAMA Central South University) ;
  • Ku, Min (Department of Computing Science University of Radboud)
  • Received : 2021.09.16
  • Accepted : 2021.12.06
  • Published : 2022.09.30
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Abstract

In this paper we study Szegö kernel projections for Hardy spaces in quaternionic Clifford analysis. At first we introduce the matrix Szegö projection operator for the Hardy space of quaternionic Hermitean monogenic functions by the characterization of the matrix Hilbert transform in the quaternionic Clifford analysis. Then we establish the Kerzman-Stein formula which closely connects the matrix Szegö projection operator with the Hardy projection operator onto the Hardy space, and we get the matrix Szegö projection operator in terms of the Hardy projection operator and its adjoint. At last, we construct the explicit matrix Szegö kernel function for the Hardy space on the sphere as an example, and get the solution to a Diriclet boundary value problem for matrix functions.

Keywords

Acknowledgement

This work was financially supported by National Natural Science Foundation of China (11601525, 12071485), Natural Science Foundation of Hunan Province (2020JJ4105).

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