Displaying similar documents to “On radial behaviour and balanced Bloch functions.”

On Bloch functions and gap series.

Daniel Girela (1991)

Publicacions Matemàtiques

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Kennedy obtained sharp estimates of the growth of the Nevanlinna characteristic of the derivative of a function f analytic and with bounded characteristic in the unit disc. Actually, Kennedy's results are sharp even for VMOA functions. It is well known that any BMOA function is a Bloch function and any VMOA function belongs to the little Bloch space. In this paper we study the possibility of extending Kennedy's results to certain classes of Bloch functions. Also, we prove some more general...

Cluster sets of analytic multivalued functions

S. Harbottle (1992)

Studia Mathematica

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Classical theorems about the cluster sets of holomorphic functions on the unit disc are extended to the more general setting of analytic multivalued functions, and examples are given to show that these extensions cannot be improved.

Asymptotic values and the growth of analytic functions in spiral domains.

James E. Brennan, Alexander L. Volberg (1993)

Publicacions Matemàtiques

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In this note we present a simple proof of a theorem of Hornblower which characterizes those functions analytic in the open unit disk having asymptotic values at a dense set in the boundary. Our method is based on a kind of ∂-mollification and may be of use in other problems as well.

Absolute values of BMOA functions.

Konstantin M. Dyakonov (1999)

Revista Matemática Iberoamericana

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The paper contains a complete characterization of the moduli of BMOA functions. These are described explicitly by a certain Muckenhoupt-type condition involving Poisson integrals. As a consequence, it is shown that an outer function with BMO modulus need not belong to BMOA. Some related results are obtained for the Bloch space.