Several Classes Of Operators On The Weighted Dirichlet Spaces

In this paper,we mainly discuss the boundedness and compactness of weighted composition operators on different weighted Dirichlet spaces,and establish the essential norm approximation of the Toeplitz operators and Hankel operators on the weighted harmonic Dirichlet spaces.In chapter 1,First,we introduce the backgrounds about weighted composition operators,Toeplitz oprators and Hankel operators.Second,we recall the preparatory knowledge.Finally,we describe the main work of this paper.In chapter 2,we give the equivalence condition of boundedness and compactness of weighted composition operators on weighted Dirichlet spaces.In chapter 3,we discuss the essential norm of Hankel operators and Toeplitz operators with symbol function in L_φ^2,1（D） and L_φ^∞,1（D）,respectively,on （?） the weighted harmonic Dirichlet space of the unit disk.We obtain approximation formulas of essential norm of Toeplitz and Hankel operators via the distance of Toeplitz and Hankel operator to the set of compact operators on （?）.