In this paper, the authors study the inclusion relations between Dirichlet type spaces DΥT and α-Bloch spaces βα by means of higher radial derivative. The strictness and the best possibility of the inclusion relat...In this paper, the authors study the inclusion relations between Dirichlet type spaces DΥT and α-Bloch spaces βα by means of higher radial derivative. The strictness and the best possibility of the inclusion relations are shown with constructive methods. Furthermore, they sharpen one of the results when Υ=n, which proves that a conjecture in [7] is true.展开更多
Let p>0 andνbe a normal function on[0,1).In this paper,several equivalent characterizations are given for which composition operators are bounded or compact on the normal weight Dirichlet type space D_(ν)^(p)(D)i...Let p>0 andνbe a normal function on[0,1).In this paper,several equivalent characterizations are given for which composition operators are bounded or compact on the normal weight Dirichlet type space D_(ν)^(p)(D)in the unit disc.展开更多
In this paper, we establish a criterion for a holomorphic function to be a pointwise multiplier of Dirichlet type spaces, and use this criterion to consider the inclusion relations among M(Dr), α-Bloch spaces and Qp ...In this paper, we establish a criterion for a holomorphic function to be a pointwise multiplier of Dirichlet type spaces, and use this criterion to consider the inclusion relations among M(Dr), α-Bloch spaces and Qp spaces.展开更多
The vector-valued Dirichlet-type spaces on the unit ball of C^n isintroduced. We discuss the pointwise multipliers of Dirichlet-type spaces. Sufficient conditions ofthe pointwise multipliers of D_(mu)~2 for 0<=mu &...The vector-valued Dirichlet-type spaces on the unit ball of C^n isintroduced. We discuss the pointwise multipliers of Dirichlet-type spaces. Sufficient conditions ofthe pointwise multipliers of D_(mu)~2 for 0<=mu <2 if n=1 or D_(mu,q)~2 for 0 =2 aregiven. Finally, Rademacher p-type space is characterized by vector-valued sequence spaces.展开更多
In this note, some conditions of composition operators on DT spaces to be bounded are given by means of Carleson measures and pointwise multipliers, for some ranges of T. The authors prove that (i) Let 1 < T n + 2...In this note, some conditions of composition operators on DT spaces to be bounded are given by means of Carleson measures and pointwise multipliers, for some ranges of T. The authors prove that (i) Let 1 < T n + 2 and 2k < T 2k + 1 (or 2k - 1 < T 2k) for some positive integer k. Suppose = ( 1,… , n) be a univalent mapping from B into itself, denote dμj(l) (z) = R(l) j (z) 2(k-l+2) (1 - z 2)2k-t+1dv(z) for l= 1, 2,… , k + 1. If μj(l)-1 are (T - 2k + 2l-4)-Carleson measures for all l, then the composition operator C on DT is bounded; (ii) Let 1 < T n + 2, = ( 1,… , n) be univalent and the Frechet derivative of -1 be bounded on (B). If R j ∈ M(DT-2) for all j, then the composition operator C on DT is bounded; (iii) Let T > n + 2 and as in (ii). If j ∈ DT for all j, then the composition operator C on DT is bounded.展开更多
基金The research is supported by NNSF of China (10271117)
文摘In this paper, the authors study the inclusion relations between Dirichlet type spaces DΥT and α-Bloch spaces βα by means of higher radial derivative. The strictness and the best possibility of the inclusion relations are shown with constructive methods. Furthermore, they sharpen one of the results when Υ=n, which proves that a conjecture in [7] is true.
基金supported by the National Natural Science Foundation of China(Grant No.11942109).
文摘Let p>0 andνbe a normal function on[0,1).In this paper,several equivalent characterizations are given for which composition operators are bounded or compact on the normal weight Dirichlet type space D_(ν)^(p)(D)in the unit disc.
文摘In this paper, we establish a criterion for a holomorphic function to be a pointwise multiplier of Dirichlet type spaces, and use this criterion to consider the inclusion relations among M(Dr), α-Bloch spaces and Qp spaces.
文摘The vector-valued Dirichlet-type spaces on the unit ball of C^n isintroduced. We discuss the pointwise multipliers of Dirichlet-type spaces. Sufficient conditions ofthe pointwise multipliers of D_(mu)~2 for 0<=mu <2 if n=1 or D_(mu,q)~2 for 0 =2 aregiven. Finally, Rademacher p-type space is characterized by vector-valued sequence spaces.
基金the Natural Science Foundation of Guangdong Province.
文摘In this note, some conditions of composition operators on DT spaces to be bounded are given by means of Carleson measures and pointwise multipliers, for some ranges of T. The authors prove that (i) Let 1 < T n + 2 and 2k < T 2k + 1 (or 2k - 1 < T 2k) for some positive integer k. Suppose = ( 1,… , n) be a univalent mapping from B into itself, denote dμj(l) (z) = R(l) j (z) 2(k-l+2) (1 - z 2)2k-t+1dv(z) for l= 1, 2,… , k + 1. If μj(l)-1 are (T - 2k + 2l-4)-Carleson measures for all l, then the composition operator C on DT is bounded; (ii) Let 1 < T n + 2, = ( 1,… , n) be univalent and the Frechet derivative of -1 be bounded on (B). If R j ∈ M(DT-2) for all j, then the composition operator C on DT is bounded; (iii) Let T > n + 2 and as in (ii). If j ∈ DT for all j, then the composition operator C on DT is bounded.
