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We present here a quite unexpected result: If the product of two quasihomogeneous Toeplitz operators on the harmonic Bergman space is equal to a Toeplitz operator , then the product is also the Toeplitz operator , and hence commutes with . From this we give necessary and sufficient conditions for the product of two Toeplitz operators, one quasihomogeneous and the other monomial, to be a Toeplitz operator.
This paper characterizes the boundedness and compactness of weighted composition operators between a weighted-type space and the Hardy space on the unit ball of ℂⁿ.
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