Composition operators on the polydisc

Research Article Weighted Composition Operators from H to the Bloch Space on the Polydisc

Let Dn be the unit polydisc of Cn. The class of all holomorphic functions with domain Dn will be denoted by H(Dn). Let φ be a holomorphic self-map of Dn, the composition operator Cφ induced by φ is defined by (Cφ f )(z) = f (φ(z)) for z ∈Dn and f ∈H(Dn). If, in addition, ψ is a holomorphic function defined on Dn, the weighted composition operator ψCφ induced by ψ and φ is defined by ψCφ(z) = ψ(...

Differences of Composition Operators on the Space of Bounded Analytic Functions in the Polydisc

This paper gives some estimates of the essential norm for the difference of composition operators induced by φ and ψ acting on the space, H∞ D , of bounded analytic functions on the unit polydisc D, where φ and ψ are holomorphic self-maps of D. As a consequence, one obtains conditions in terms of the Carathéodory distance on D that characterizes those pairs of holomorphic self-maps of the polyd...

High-order Green operators on the disk and the polydisc

The Essential Norms of Composition Operators between Generalized Bloch Spaces in the Polydisc and Their Applications

Let Un be the unit polydisc of Cn and φ = (φ1, . . . ,φn) a holomorphic self-map of Un. p(Un), p 0 (U n), and p 0∗(U n) denote the p-Bloch space, little p-Bloch space, and little star p-Bloch space in the unit polydisc Un, respectively, where p,q > 0. This paper gives the estimates of the essential norms of bounded composition operators Cφ induced by φ between p(Un) ( p 0 (U n) or p 0∗(U n)) an...

Compact Differences of Composition Operators from Bloch Space to Bounded Holomorphic Function Space in the Polydisc

Abstract. Let φ and ψ be holomorphic self-maps of the unit polydisc U in the n-dimensional complex space, and denote by Cφ and Cψ the induced composition operators. This paper gives some simple estimates of the essential norm for the difference of composition operators Cφ − Cψ from Bloch space to bounded holomorphic function space in the unit polydisc. Moreover the compactness of the difference...