The Berezin transform on the Toeplitz algebra
This paper studies the boundary behavior of the Berezin transform on the C*-algebra generated by the analytic Toeplitz operators on the Bergman space.
Hilbert transform, Toeplitz operators and Hankel operators and invariant A weights.
In this paper, several sufficient conditions for boundedness of the Hilbert transform between two weighted L-spaces are obtained. Invariant A weights are obtained. Several characterizations of invariant A weights are given. We also obtain some sufficient conditions for products of two Toeplitz operators of Hankel operators to be bounded on the Hardy space of the unit circle using Orlicz spaces and Lorentz spaces.
m-Berezin transform and compact operators.
m-Berezin transforms are introduced for bounded operators on the Bergman space of the unit ball. The norm of the m-Berezin transform as a linear operator from the space of bounded operators to L is found. We show that the m-Berezin transforms are commuting with each other and Lipschitz with respect to the pseudo-hyperbolic distance on the unit ball. Using the m-Berezin transforms we show that a radial operator in the Toeplitz algebra is compact iff its Berezin transform vanishes on the boundary...
Page 1