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Pluriharmonic symbols of commuting Toeplitz type operators. (English) Zbl 0881.47015

Summary: Certain Toeplitz type operators acting on the Bergman space \(A^1\) of the unit ball are considered and pluriharmonic symbols of commuting Toeplitz type operators are characterized by using \({\mathcal M}\)-harmonic function theory.

MSC:

47B35 Toeplitz operators, Hankel operators, Wiener-Hopf operators
32A37 Other spaces of holomorphic functions of several complex variables (e.g., bounded mean oscillation (BMOA), vanishing mean oscillation (VMOA))
47B38 Linear operators on function spaces (general)
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References:

[1] DOI: 10.1007/BF01193761 · Zbl 0697.47023
[2] Rudin, Function theory in the unit ball of C (1980) · Zbl 0495.32001
[3] DOI: 10.1007/BF02568394 · Zbl 0816.31004
[4] DOI: 10.1007/BF01194925 · Zbl 0733.47027
[5] DOI: 10.1006/jfan.1993.1018 · Zbl 0771.32006
[6] DOI: 10.2307/2374685 · Zbl 0669.47017
[7] Choe, Illinois J. Math. 37 pp 424– (1993)
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