Mantoiu M., Purice R. Hardy Type Estimations with Exponential Weights for Operators of Convolution with Analytic Functions (328K, Postscript) ABSTRACT. In this paper we develop a general procedure to prove Hardy type estimations for an operator that admits a conjugate operator, starting from the Mourre estimation. We use this method for operators of convolution with analytic functions, obtaining Hardy type estimations with exponential weights, for sufficiently small exponents.