LAUSR

Abstract We study the complex symmetric structure of weighted composition operators of the form W ψ , φ on the Hilbert space H γ ( D ) of holomorphic functions over the open unit disk D with reproducing kernels K w ( γ ) = ( 1 − w ‾ z ) − γ , where γ ∈ N . First, we consider conjugations on H γ ( D ) of the form A u , v f = u ⋅ f ∘ v ‾ ‾ (such conjugations are also known as weighted composition conjugations) and characterize them into two classes, denoted by C 1 and C 2 . Then, we obtain explicit conditions for W ψ , φ when it is C 1 -symmetric and C 2 -symmetric respectively.