Essential norms of weighted composition operators between Zygmund-type spaces and Bloch-type spaces

Abstract

We investigate the boundedness of weighted composition operator uCφ mapping the Zygmund-type space Z α into the Bloch-type space B β . Then we give essential norm estimates of such an operator in terms of u and φ .

Closed range properties of Li–Stević integral-type operators between Bloch-typespaces and their essential norms

“…In many papers, the results concerning essential norms are given in terms of "almost" equalities, not "exact" equalities. See, for example, [18,19,22,23]. It is worth mentioning here that the results of Theorems 3.1,3.2,and 3.3 and Corollary 3.4 are given in terms of "exact" equalities, not "almost" equalities.…”

Essential norms of weighted differentiation composition operators between Zygmund type spaces and Bloch type spaces

“…By applying these facts and using [4, Lemma 2.1], our results in this paper containing terms of the type ω(z) ν(ϕ(z)) |u(z)| can be restated in terms of u and ϕ n . See, for example, [1,16] for these types of results. Remark 3.7.…”

“…Weighted composition operator uC ϕ from Zygmund type spaces to Bloch type spaces has been studied in [2]. See also [6,15,16], for more results on weighted composition operators between certain spaces of analytic functions. Let ϕ be an analytic selfmap of D, u ∈ H(D) and k ∈ N. The weighted differentiation composition operator…”

New Characterizations for the Essential Norms of Generalized Weighted Composition Operators between Zygmund-Type Spaces

“…Weighted composition operators appear in the study of dynamical systems, and also, it is known that isometries on many analytic function spaces are of the canonical forms of weighted composition operators. Operator theoretic properties of (weighted) composition operators have been studied by many authors between different classes of analytic function spaces (see, for example, [4,5,8,9], and the references therein).…”