We study a correspondence L between some classes of functions holomorphic in the unit disc and functions holomorphic in the left halfplane. This correspondence is such that for every f and w ∈ ℍ, exp(L(f)(w)) = f(expw). In particular, we prove that the famous class S of univalent functions on the unit disc is homeomorphic via L to the class S(ℍ) of all univalent functions g on ℍ for which g(w+2πi) = g(w) + 2πi and $li{m}_{Rez\to -\infty }(g\left(w\right)-w)=0$.

We present new sharp embedding theorems for mixed-norm analytic spaces in pseudoconvex domains with smooth boundary. New related sharp results in minimal bounded homogeneous domains in higher dimension are also provided. Last domains we consider are domains which are direct generalizations of the well-studied so-called bounded symmetric domains in ${ℂ}^n.$ Our results were known before only in the very particular case of domains of such type in the unit ball. As in the unit ball case, all our proofs are...

We construct an infinite uniform Frostman Blaschke product B such that B ∘ B is also a uniform Frostman Blaschke product. We also show that the set of uniform Frostman Blaschke products is open in the set of inner functions with the uniform norm.

We shall prove, using the result from our previous paper [Ann. Polon. Math. 88 (2006)], that for a quadratic polynomial mapping Q of ℝ² only the geometric shape of the critical set of Q determines whether the complexification of Q can be extended to an endomorphism of ℂℙ². At the end of the paper we describe some interesting classes of quadratic polynomial mappings of ℝ² and give some examples.