Products of composition, multiplication and radial derivative operators from logarithmic Bloch spaces to weighted-type spaces on the unit ball

Abstract

Let H(B) denote the space of all holomorphic functions on the unit ball B of C n , ψ ∈ H(B) and ϕ be a holomorphic self-map of B. Let C ϕ , M ψ and R denote the composition, multiplication and radial derivative operators, respectively. In this paper, we characterize the boundedness and compactness of linear operators induced by products of these operators from logarithmic Bloch spaces to weighted-type spaces on the unit ball.

Product Type Operators Involving Radial Derivative Operator Acting between Some Analytic Function Spaces

“…For more information about the radial derivative operator we refer to [11,12] and the references therein. Using radial derivative operator and φ 1 , φ 2 , φ 3 ∈ H(B m ), Liu and Yu in [13] studied the extension of the operator T φ 1 ,φ 2 ,ξ which is denoted by T φ 1 ,φ 2 ,φ 3 ,ξ and defined as…”

“…In particular, by setting φ 2 (z) ≡ φ 3 (z) ≡ 0, the operator T φ 1 ,φ 2 ,φ 3 ,ξ get reduced to W φ 1 ,ξ . Similarly, for φ 1 (z) ≡ φ 3 (z) ≡ 0, the operator T φ 1 ,φ 2 ,φ 3 ,ξ get reduced to W φ 2 ,ξ R. The above defined operator can be found in [13] and the references therein. Various product-type operators have been studied for spaces of analytic functions on the unit disk.…”

“…For this one can refer [14][15][16][17][18][19]. Product-type operators for the unit ball have also been considered by various experts which can be found in [5,13,[20][21][22][23]. Operators involving radial derivative have been considered in many papers some of which are [6,24,25] and the references therein.…”

Products of Composition, Multiplication and Iterated Differentiation Operators Between Banach Spaces of Holomorphic Functions

“…, ψ n }. The sum operator for n = 1 has been studied in several papers, see [10][11][12][17][18][19][20]. Recall that the Bell polynomial for n, k ∈ N 0 is defined as…”

Generalized weighted composition operators from H∞ to the logarithmic Bloch space

“…In [1], Attele showed that the Hankel operator H f is bounded on the Bergman space A 1 if and only if f ∈ LB, where H f = (I − P)( f ), I is the identity operator and P is the Bergman projection from L 1 into A 1 . See, for example, [3,6,11,17,26,27,29] for some results on logarithmic spaces and operators on them.…”