## Toeplitz operators on harmonic Bergman spaces.(English)Zbl 0902.47026

Summary: We study Toeplitz operators on the harmonic Bergman space $$b^p(B)$$, where $$B$$ is the open unit ball in $$\mathbb{R}^n$$ $$(n\geq 2)$$, for $$1< p<\infty$$. We give characterizations for the Toeplitz operators with positive symbols to be bounded, compact, and in Schatten classes. We also obtain a compactness criteria for the Toeplitz operators with continuous symbols.

### MSC:

 47B35 Toeplitz operators, Hankel operators, Wiener-Hopf operators 46J15 Banach algebras of differentiable or analytic functions, $$H^p$$-spaces
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### References:

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