Abstract
In this paper, we consider the Toeplitz operators and little Hankel operators on the Dirichletspace D of the unit disc D. By Berezin type transform, the invariant subspaces of Toeplitz operators, asymptoticmultiplicative property of the Berezin type symbols of Toeplitz operators and solvability of the Riccati equationsof Toeplitz operators are discussed. We also obtained a sufficient condition for invertibility of Toeplitz operatorsand little Hankel operators in terms of Berezin transform. Moreover, the Hankel operators and Berezin transformare used to characterize compactness of operators 2 Tuv - TuTv - TvTu for functions u and v in L 2,1.
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