Properties of Commutativity of Dual Toeplitz Operators on the Orthogonal Complement of Pluriharmonic Dirichlet Space over the Ball. (20th January 2016) - Hu, Yinyin; Lu, Yufeng; Yu, Tao
Abstract : We completely characterize the pluriharmonic symbols for (semi)commuting dual Toeplitz operators on the orthogonal complement of the pluriharmonic Dirichlet space in Sobolev space of the unit ball. We show that, for f and g pluriharmonic functions, S f S g = S g S f on ( D h ) ⊥ if and only if f and g satisfy one of the following conditions: ( 1 ) both f and g are holomorphic; ( 2 ) both f ¯ and g ¯ are holomorphic; ( 3 ) there are constants α and β, both not being zero, such that α f + β g is constant.