Commuting Toeplitz Operators on the Pluriharmonic Bergman Space

Toeplitz Operators on Harmonic Fock Spaces with Radial Symbols

“…There have been some results of the Toeplitz operator T a in harmonic Bergman space; please refer to [16][17][18]. In the paper [16], Guo and Zheng characterized compact Toeplitz operators in the unit disk D. In [18], by using the system of integral equations, Lee characterized the commuting Toeplitz operators of holomorphic symbols and pluriharmonic symbols in pluriharmonic Bergman space.…”

“…In the paper [16], Guo and Zheng characterized compact Toeplitz operators in the unit disk D. In [18], by using the system of integral equations, Lee characterized the commuting Toeplitz operators of holomorphic symbols and pluriharmonic symbols in pluriharmonic Bergman space. In addition, Lee proved in [17] the commutativity of an operator with a radial symbol and an operator with a pluriharmonic symbol in pluriharmonic Bergman space. In the papers [7,[19][20][21][22], several mathematicians analyzed the influence of the radial component of a symbol of the spectral, compactness and Fredholm properties of Toeplitz operators on Bergman space or Fock space.…”