Analytic Characterization of t-Quasicircles and Conformal Mappings onto t-Quasidisks

In this paper, we introduce a new class of mappings, termed $(ρ,t)$-quasisymmetric mappings, which generalizes the classical concept of quasisymmetric mappings. Using this broader class of mappings, we provide an analytic characterization of t-quasicircles. This result can be viewed as a t-quasisymmetric analogue of a classical theorem by Tukia and Väisälä {TV}. Furthermore, we study conformal mappings from the unit disk D onto t-quasidisks and show that their boundary values are "almost`` (ρ,t²)-quasisymmetric. This result extends the Quasicircle Theorem to the case of t-quasicircles.