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.
We characterize complex measures μ on the unit ball of C n , for which the general Toeplitz operator T α μ is bounded or compact on the analytic Besov spaces B p B n , also on the minimal Möbius invariant Banach spaces B 1 B n in the unit ball B n .
The present manuscript gives analytic characterizations and interesting technique that involves the study of general
ϖ
-Besov classes of analytic functions by the help of analytic
ϖ
-Bloch functions. Certain special functions significant in both
ϖ
-Besov-norms and
ϖ
-Bloch norms framework and to introduce new important families of analytic classes. Interesting motivation of this concerned paper is to construct some new analytic function classes of general
ϖ
-Besov-type spaces via integrals on concerned functions view points. The introduced analytic
ϖ
-Bloch and
ϖ
-Besov type of functions with some interesting properties for these classes of function spaces are established within the constructions of their norms. Using the defined analytic function spaces, various important relations are also derived.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.