Dual Hankel operators with harmonic symbols on the orthogonal complement of Dirichlet space
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In this paper, we study some algebraic properties of dual Hankel operators with harmonic symbols on the orthogonal complement of the Dirichlet space in the Sobolev space. We first investigate the boundedness and compactness of dual Hankel operators. Next, we completely characterize the commutativity of two dual Hankel operators, or a dual Hankel and a dual Toeplitz operator. The problem of when a product of two dual Hankel operators is another dual Hankel operator or dual Toeplitz operator is studied.
Abstract
In this paper, we study some algebraic properties of dual Hankel operators with harmonic symbols on the orthogonal complement of the Dirichlet space in the Sobolev space. We first investigate the boundedness and compactness of dual Hankel operators. Next, we completely characterize the commutativity of two dual Hankel operators, or a dual Hankel and a dual Toeplitz operator. The problem of when a product of two dual Hankel operators is another dual Hankel operator or dual Toeplitz operator is studied.