Results on weighted sharing of values for meromorphic functions
We prove some results on uniqueness of functions with three shared values. Our results improve those given by H. X. Yi, I. Lahiri, T. C. Alzahary & H. X. Yi, and other authors.
Riemann–Stieltjes operators between Bergman-type spaces and -Bloch spaces.
Riemann--Stieltjes operators between vector-valued weighted Bloch spaces.
Rigidity of harmonic measure
Let J be the Julia set of a conformal dynamics f. Provided that f is polynomial-like we prove that the harmonic measure on J is mutually absolutely continuous with the measure of maximal entropy if and only if f is conformally equivalent to a polynomial. This is no longer true for generalized polynomial-like maps. But for such dynamics the coincidence of classes of these two measures turns out to be equivalent to the existence of a conformal change of variable which reduces the dynamical system...
Rotation-automorphic functions near the boundary.