On Bloch functions and gap series.
On Bloch functions and gap series.
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 results...
On Bloch functions and normal functions.
On Entire Functions with Infinite Domains of Normality.
On Extreme Bloch Functions with Prescribed Critical Points.
On groups and normal polymorphic functions.
On Normal Meromorphic Functions.
On spaces and pseudoanalytic extension.
On radial behaviour and balanced Bloch functions.
A Bloch function g is a function analytic in the unit disk such that (1 - |z|2) |g' (z)| is bounded. First we generalize the theorem of Rohde that, for every bad Bloch function, g(rζ) (r → 1) follows any prescribed curve at a bounded distance for ζ in a set of Hausdorff dimension almost one. Then we introduce balanced Bloch functions. They are characterized by the fact that |g'(z)| does not vary much on each circle {|z| = r} except for small exceptional arcs. We show e.g. that∫01 |g'(rζ)|dr <...
On rotation-automorphic functions.
On the angular boundedness of Bloch functions.
On the angular limits of Bloch functions.
This paper contains a method to associate to each function f in the little Bloch space another function f* in the Bloch space in such way that f has a finite angular limit where f* is radially bounded. The idea of the method comes from the theory of lacunary series. An application to conformal mapping from the unit disc to asymptotically Jordan domains is given.
On the coefficient multipliers of Bloch and Hardy spaces in a polydisk.
On the five-point theorems due to Lappan
By using an extension of the spherical derivative introduced by Lappan, we obtain some results on normal functions and normal families, which extend Lappan's five-point theorems and Marty's criterion, and improve some previous results due to Li and Xie, and the author. Also, another proof of Lappan's theorem is given.
On the law of iterated logarithm for Bloch functions
On the multiplicative behavior of Bloch functions.
On the normal meromorphic functions.
On the Normality of Derivatives of Functions.
On zeros of normal functions.