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Product equivalence of quasihomogeneous Toeplitz operators on the harmonic Bergman space

100%

Dong X.-T., Zhou Z.-H.

Studia Mathematica

2013

tom 219

nr 2

163-175

We present here a quite unexpected result: If the product of two quasihomogeneous Toeplitz operators $T_{f}T_{g}$ on the harmonic Bergman space is equal to a Toeplitz operator $T_{h}$, then the product $T_{g}T_{f}$ is also the Toeplitz operator $T_{h}$, and hence $T_{f}$ commutes with $T_{g}$. 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.

Weighted composition operators between a weighted-type space and the Hardy space on the unit ball

81%

Zhou Z.-H., Liang Y.-X., Dong X.-T.

Annales Polonici Mathematici

2012

tom 104

nr 3

309-319

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.

Ograniczanie wyników

1 Annales Polonici Mathematici

1 Studia Mathematica

2 Dong X.-T.

2 Zhou Z.-H.

1 Liang Y.-X.

1 2013

1 2012

Wyniki wyszukiwania

Product equivalence of quasihomogeneous Toeplitz operators on the harmonic Bergman space

Weighted composition operators between a weighted-type space and the Hardy space on the unit ball