Hankel Operators On Dirichlet Space

In H∞ control problems, the famous Nehari theory turnedthe model-matching problems into Nehari problems, that is to calculate (or estimate) the norm of Hankel operators. In H∞ control problems, the Hankel operators are often compactor have finite rank, but for general symbols the corresponding Hankel operators may not be compact. According to this fact, it is natural to discuss for what symbols the corresponding Hankel operators are compact. In the past a few years, the compactness of Hankel operators on Hardy and Bergman spaces have been discussed extensively. In this paper, the problems about Hankel operators on Dirichlet spaces are discussed. Thecompactness of Hankel operators with symbols in C1(D)onDirichlet spaces are proved, and the criterion for compact little Hankel operators on Dirichllet spaces are discussed.