Generalized Composition Operators From Generalized Weighted Bergman Spaces to Bloch Type Spaces

Abstract

Abstract. Let H(B) denote the space of all holomorphic functions on the unit ball B of + n . Let ϕ = (ϕ 1 , . . . , ϕ n ) be a holomorphic self-map of B and g ∈ H(B) with g(0) = 0. In this paper we study the boundedness and compactness of the generalized composition operatordt t from generalized weighted Bergman spaces into Bloch type spaces.

Product of composition and differentiation operators and closures of weighted Bergman spaces in Bloch type spaces

“…It is well known that, for any positive integer m, there exist two functions f 1 , f 2 ∈ B α such that (see [36])…”

Boundedness and essential norm of an integral-type operator on a Hilbert–Bergman-type spaces

“…Some product-type generalizations of the operator on the unit disc were later introduced and studied, for example, in [5], while the corresponding operator for the case of the unit ball was introduced in [6] and later studied in many papers to mention, for example, [7] (for the case of the polydisc, see, e.g., [8]). For some further generalizations, related operators, and related results, see also [9][10][11] and the references therein. We would like to point out that a great majority of these papers are devoted to characterizing some function-theoretic properties of these operators in terms of the involved symbols.…”

Generalized Composition Operators fromℬμSpaces toQK,ω(p,Li1, Ma2 2014Abstract and Applied Analysis3030View full textAdd to dashboardCite

“…Madigan and Matheson (see [1]) gave a characterization of the compact composition operators on the Bloch space B. For more details, see [4][5][6][7][8][9][10][11][12]. In [13], Li and Stević defined the generalized composition operator as follows:…”

“…In [19], generalized composition operator acting from Bloch-type spaces to mixed-norm space was studied. In [12], generalized composition operators from generalized weighted Bergman spaces to Bloch type spaces were investigated. In [20], generalized composition operators and Volterra composition operators on Bloch spaces on the unit ball were studied.…”