A sharp weak-Schatten link theorem with optimal logarithmic loss, plus a profile-transfer calculus, yields necessary-and-sufficient Schatten-class convergence thresholds for singular Wick multipliers on groups, Z^D, and T^D.
Pansu, Croissance des boules et des géodésiques fermées dans les nilvariétés,Ergodic Theory Dynam
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Algebraic Transfer for Operator-Valued Gaussian Chaoses:Oriented Schatten Profiles and Singular Wick Multipliers
A sharp weak-Schatten link theorem with optimal logarithmic loss, plus a profile-transfer calculus, yields necessary-and-sufficient Schatten-class convergence thresholds for singular Wick multipliers on groups, Z^D, and T^D.