In this paper we are concerned with an extension operator Φ n,α,β that provides a way of extending a locally univalent function f on the unit disc U to a locally biholomorphic mapping F ∈ H(B n ). By using the method of Loewner chains, we prove that if f can be embedded as the first element of a g-Loewner chain on the unit disc, whereAlso, if f is spirallike of type δ and order γ on U , where δ ∈ (−π/2, π/2) and γ ∈ (0, 1), then F = Φ n,α,β (f) is spirallike of type δ and order γ on B n . We also obtain a subordination preserving result under the operator Φ n,α,β and we consider some radius problems associated with this operator.

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