Some Algebra Properties Of Toeplitz And Hankel Operators On Harmonic Spaces

To describe the properties of operators by their symbol functions is an important propose for operator theory.In this paper,We study the commutativity,products,Finite ranks,zero product properties of Toeplitz and Hankel operators on harmonic Dirichlet space and harmonic Bergman space.1,In the first chapter,we introduce basic information of the function spaces.We also introduce Toeplitz operators and(small)Hankel operators with their background and current status of related research.2,In the second chapter,we study the commuting,products,finite ranks and compact prob-lems for Toeplitz and(small)Hankel operators on Harmonic Dirichlet space of the unit disk with general bounded symbols.We also study commuting and products problems of two(small)Hankel operators.3,In the third chapter,We study zero products problem and finite ranks of the Brown-Halmos type results involving products of Toeplitz operators acting on the harmonic Bergman space.