On the classical Bergman space,Toeplitz operators with radial symbols are diagonal and those operators commute.However,on the n-analytic Bergman space A_(n)^(2)(D)when n≥2,the case is different.In this paper,our focu...On the classical Bergman space,Toeplitz operators with radial symbols are diagonal and those operators commute.However,on the n-analytic Bergman space A_(n)^(2)(D)when n≥2,the case is different.In this paper,our focus is on the problem of commuting Toeplitz operators with quasihomogeneous symbols,specifically in the context of the function space A_(2)^(2)(D).We show a kind of block matrice expression of Toeplitz operators on A_(2)^(2)(D).Based on the block expression,we give several important properties.Our results indicate that in some cases,two Toeplitz operators are commutative if and only if both operators are analytic or differ by a constant multiple.展开更多
基金Supported by NSFC(Grant Nos.12371134 and 12031002)SDNSFC(Grant Nos.ZR2021MA015 and ZR2020MA009)。
文摘On the classical Bergman space,Toeplitz operators with radial symbols are diagonal and those operators commute.However,on the n-analytic Bergman space A_(n)^(2)(D)when n≥2,the case is different.In this paper,our focus is on the problem of commuting Toeplitz operators with quasihomogeneous symbols,specifically in the context of the function space A_(2)^(2)(D).We show a kind of block matrice expression of Toeplitz operators on A_(2)^(2)(D).Based on the block expression,we give several important properties.Our results indicate that in some cases,two Toeplitz operators are commutative if and only if both operators are analytic or differ by a constant multiple.
