Zygmund-type Spaces Research Articles

DERIVATIVE-FREE CHARACTERIZATIONS OF COMPACT GENERALIZED COMPOSITION OPERATORS BETWEEN ZYGMUND TYPE SPACES

AbstractWe give derivative-free characterizations for bounded and compact generalized composition operators between (little) Zygmund type spaces. To obtain these results, we extend Pavlović’s corresponding result for bounded composition operators between analytic Lipschitz spaces.

Integral-Type Operators from Spaces to Zygmund-Type Spaces on the Unit Ball

Let denote the space of all holomorphic functions on the unit ball . This paper investigates the following integral-type operator with symbol , , , , where is the radial derivative of . We characterize the boundedness and compactness of the integral-type operators from general function spaces to Zygmund-type spaces , where is normal function on .

Integral-type operators from iterated logarithmic Bloch spaces to Zygmund-type spaces

Let H ( B ) denote the space of all holomorphic functions on the unit ball B of C n and R h ( z ) = ∑ j = 1 n z j ∂ h ∂ z j ( z ) the radial derivative of h. In this paper we study the boundedness and compactness of the following integral operator: T g ( f ) ( z ) = ∫ 0 1 f ( tz ) R g ( tz ) dt t , f ∈ H ( B ) , z ∈ B , from iterated logarithmic Bloch spaces to Zygmund-type spaces.

Integral-type operators from Bloch-type spaces to Zygmund-type spaces

Let H ( B ) denote the space of all holomorphic functions on the unit ball B ⊂ C n . This paper investigates the following integral-type operator with symbol g ∈ H ( B ) T g ( f ) ( z ) = ∫ 0 1 f ( tz ) R g ( tz ) dt t , f ∈ H ( B ) , z ∈ B , where R g ( z ) = ∑ j = 1 n z j ∂ g ∂ z j ( z ) is the radial derivative of g. The boundedness and compactness of the operator T g from Bloch-type spaces to Zygmund-type spaces are studied.

Composition Operators from the Hardy Space to the Zygmund-Type Space on the Upper Half-Plane

Here we introduce thenth weighted space on the upper half-planeΠ+={z∈ℂ:Im z>0}in the complex planeℂ. For the casen=2, we call it the Zygmund-type space, and denote it by𝒵(Π+). The main result of the paper gives some necessary and sufficient conditions for the boundedness of the composition operatorCφf(z)=f(φ(z))from the Hardy spaceHp(Π+)on the upper half-plane, to the Zygmund-type space, whereφis an analytic self-map of the upper half-plane.