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Finite rank product theorems for Toeplitz operators on the half-space. (English) Zbl 1173.47017

The authors study products of Toeplitz operators with harmonic symbols acting on the harmonic Bergman space over the half plane in \(\mathbb{R}^n\). The main result of the paper states that, if the product of a finite number of Toeplitz operators, whose harmonic symbols have certain boundary smoothness, has finite rank, then one of the symbols must be identically zero. Note that the number of factors is related to the dimension \(n\).

MSC:

47B35 Toeplitz operators, Hankel operators, Wiener-Hopf operators
46E30 Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
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References:

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