In this note we characterise the bounded composition operators on the anisotropic Dirichlet-type spaces Da⃗(D²) induced by holomorphic self maps of the bi-disc D² of the form Φ(z₁,z₂)=(φ₁(z₁),φ₂(z₂)) via the respective generalised Nevanlinna counting functions of both symbols. We also characterise the bounded composition operators from A²(D²) to D(D²) for general self maps of the bidisc via a Carleson-type condition.
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Athanasios Beslikas (2024) studied this question.
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