# Bulletin of theKorean Mathematical SocietyBKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc.

Published online July 13, 2022

## Szego Projections for Hardy Spaces in Quaternionic Clifford Analysis

Fuli He, Song Huang, and Min Ku

Central South University, University of Radboud

### Abstract

In this paper we study Szego Kernel projections for Hardy spaces in quaternionic Clifford Analysis. At first we introduce the matrix Szego 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 Szego projection operator with the Hardy projection operator onto the Hardy space, and we get the matrix Szego projection operator in terms of the Hardy projection operator and its adjoint. At last, we construct the explicit matrix Szego 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: Sezgo projections; Quaternionic Clifford Analysis; Hardy space; Matrix function.

MSC numbers: 30G35; 15A66; 30C40; 31A25; 31B10