The pluriharmonic Hardy space and Toeplitz Operators

2016/12/07 by Sang, Yuanqi, Ding, Xuanhao
#30H10 #47B35 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1612.02125

Abstract

Compared with harmonic Bergman spaces, this paper introduces a new function space which is called the pluriharmonic Hardy space h²(\mathbbT²). We character (semi-) commuting Toeplitz operators on h²(\mathbbT²) with bounded pluriharmonic symbols. Interestingly, these results are quite different from the corresponding properties of Toeplitz operators on Hardy spaces, Bergman spaces and harmonic Bergman spaces. Our method for Toeplitz operators on h²(\mathbbT²) gives new insight into the study of commuting Toeplitz operators on harmonic Bergman spaces.

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