A Representation of Matrix-Valued Harmonic Functions by the Poisson Integral of Non-commutative BMO Functions

Cheng Chen; Guixiang Hong; Wenhua Wang

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A Representation of Matrix-Valued Harmonic Functions by the Poisson Integral of Non-commutative BMO Functions

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arxiv 2309.11752 v2 pith:HFMYNFX5 submitted 2023-09-21 math.CA math.FA

Cheng Chen , Guixiang Hong , Wenhua Wang This is my paper · ORCID

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keywords functionsnon-commutativeharmonicintegralmatrix-valuedpoissonanalogueauthors

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In this paper, the authors study the matrix-valued harmonic functions and characterize them by the Poisson integral of functions in non-commutative BMO (bounded mean oscillation) spaces. This provides a very satisfactory non-commutative analogue of the beautiful result due to Fabes, Johnson and Neri [Indiana Univ. Math. J. {\bf25} (1976) 159-170; MR0394172].

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