We study in this paper analytic Schur multipliers on (Formula Presented), i.e. Schur multipliers on (Formula Presented) and (Formula Presented) that are boundary-value functions of functions analytic in (Formula Presented). Such Schur multipliers are important when studying properties of functions of maximal dissipative operators and contrac tions under perturbation. We show that if the boundary-value function of a Schur multiplier has certain regularity properties, then it can be represented as an element of the Haagerup tensor product of spaces of analytic functions with similar regularity properties. © 2026 American Mathematical Society