Commutativity of Toeplitz Operator and Small Hankel Operator on Three-disk Hardy Spaces
The commutativity problem of Toeplitz operator is a hot topic in operator theory,which has different manifestations in different function spaces.In this paper,the equation T∗f Hg = Hg Tf∗ is studied on the Hardy space of three disks,and the sufficient and necessary conditions are given when f and g are general functions and special functions.Then,aiming at the commutativity problem of Toeplitz operator and small Hankel operator on three disks,a set of normal orthogonal basis of three disks is taken by using multiple Fourier decomposition of the function.The necessary and sufficient conditions for commutative Toeplitz operator and small Hankel operator are obtained by operating operators on normal orthogonal basis.A similar conclusion holds for n-disk Hardy Spaces.