Composition operators in hyperbolic general Besov-type spaces

Abstract

In this paper we introduce natural metrics in the hyperbolic α-Bloch and hyperbolic general Besov-type classes F * (p, q, s). These classes are shown to be complete metric spaces with respect to the corresponding metrics. Moreover, compact composition operators C φ acting from the hyperbolic α-Bloch class to the class F * (p, q, s) are characterized by conditions depending on an analytic self-map φ : D → D. RESUMEN En este artículo introducimos una métrica natural en las clases hiperbólicas α-Bloch y tipo Besov generales. Estas clases se muestra que son espacios métricos completos respecto de las métricas correspondientes. Además se caracterizan los operadores de composición compactos C φ que actúan desde las clases hiperbólicas α-Bloch en la clase F * (p, q, s) por condiciones que dependen de la autoaplicación analítica φ : D → D.

Composition Operator, Boundedness, Compactness, Hyperbolic Bloch-Type Space βμ∗, Hyperbolic-Type Space

“…Composition operators from the Bloch-type space into some other analytic function spaces have been much investigated in recent years, see [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19] and references therein. Also, there are many works concerning composition operators from hyperbolic Bloch type spaces into some other hyperbolic classes, see [20][21][22][23]. This work is intended to characterize the boundedness and compactness of composition operators C φ from hyperbolic Bloch type spaces β * μ into hyperbolic type spaces Q * K,p,q .…”

Certain Classes of Operators on Some Weighted Hyperbolic Function Spaces

“…Dealing with corresponding concerned spaces of weighted functions on the disk Δ, essential properties of the new type of operators are discussed. ere are some certain attempts to study hyperbolic function spaces (see [1][2][3][4][5][6][7][8][9][10][11][12][13][14] and others). Most research studies were on composition operators.…”

Hadamard Gaps and <i>N</i><sub>k</sub>-type Spaces in the Unit Ball

“…Clearly, if  spaces of holomorphic function in the case of the unit disk has been studied quite well in [4] and [5].…”