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On Some Correspondence between Holomorphic Functions in the Unit Disc and Holomorphic Functions in the Left Halfplane

Ewa Ligocka (2009)

Bulletin of the Polish Academy of Sciences. Mathematics

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 l i m R e z - ( g ( w ) - w ) = 0 .

On some new sharp embedding theorems in minimal and pseudoconvex domains

Romi F. Shamoyan, Olivera R. Mihić (2016)

Czechoslovak Mathematical Journal

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 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...

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