Let ,B and Qβ be the weighted Nevanlinna space, the Bloch space and the Q space, respectively. Note that B and are Möbius invariant, but is not. We characterize, in function-theoretic terms, when the composition operator induced by an analytic self-map ϕ of the unit disk defines an operator , , which is bounded resp. compact.
On étudie la dimension moyenne de l’espace de courbes -Brody à valeurs dans deux surfaces complexes : d’abord pour des surfaces de Hopf, et ensuite pour privé d’une droite. On montre dans le premier cas que la dimension moyenne est nulle via une borne sur la croissance des fonctions holomorphes faisant apparaître le lemme de la dérivée logarithmique. Pour montrer la positivité dans le deuxième exemple, on relève de la droite à son complémentaire un espace de courbes de Brody de dimension moyenne...
We investigate the uniqueness problem of entire functions that share two polynomials with their th derivatives and obtain some results which improve and generalize the recent result due to Lü and Yi (2011). Also, we exhibit some examples to show that the conditions of our results are the best possible.
Applying the normal family theory and the theory of complex differential equations, we obtain a uniqueness theorem for entire functions that share a function with their first and second derivative, which generalizes several related results of G. Jank, E. Mues & L. Volkmann (1986), C. M. Chang & M. L. Fang (2002) and I. Lahiri & G. K. Ghosh (2009).
Motivated by some recent results by Li and Stević, in this paper we prove that a two-parameter family of Cesàro averaging operators is bounded on the Dirichlet spaces . We also give a short and direct proof of boundedness of on the Hardy space for 1 < p < ∞.
A holomorphic family , |z|<1, of injections of a compact set E into the Riemann sphere can be extended to a holomorphic family of homeomorphisms , |z|<1, of the Riemann sphere. (An earlier result of the author.) It is shown below that there exist extensions which, in addition, commute with some holomorphic families of holomorphic endomorphisms of , |z|<1 (under suitable assumptions). The classes of covering maps and maps with the path lifting property are discussed.
In this paper we mainly estimate the hyper-order of an entire function which shares one function with its derivatives. Some examples are given to show that the conclusions are meaningful.