A Representation of Matrix-Valued Harmonic Functions by the Poisson Integral of Non-commutative BMO Functions
Cheng Chen, Guixiang Hong, Wenhua Wang
TL;DR
This paper characterizes matrix-valued harmonic functions using the Poisson integral of non-commutative BMO functions, extending classical harmonic analysis results into the non-commutative setting.
Contribution
It provides a non-commutative analogue of a classical harmonic analysis result, linking matrix-valued harmonic functions with non-commutative BMO spaces.
Findings
Characterization of matrix-valued harmonic functions via Poisson integrals.
Extension of classical harmonic analysis results to non-commutative spaces.
Establishment of a non-commutative BMO framework for harmonic functions.
Abstract
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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Taxonomy
TopicsAdvanced Harmonic Analysis Research · Holomorphic and Operator Theory · Advanced Differential Geometry Research