Some Characterizations of Weighted Holomorphic Function Classes by Univalent Function Classes

Abstract

Some characterizations of $Q_{K,\omega }\left(p,q\right)-$ type classes of holomorphic functions by Schwarzian derivatives with known conformal-type mappings are introduced in the present manuscript. Moreover, the action of the pre-Schwarzian derivatives on $Q_{K,\omega }\left(p,q\right)-$ type classes, typically the univalent ones by using concerned Carleson-type measures, is investigated. In addition, we reveal important characterizations of some concerned weighted analytic-type spaces with the known Schwarzian derivatives evolving certain $Q-$ type of concerned function class for a high utility toward practical and feasible application of concerned domains.