In this paper, a new class of Bayesian lower bounds is proposed. Derivation of the proposed class is performed via projection of each entry of the vector-function to be estimated on a closed Hilbert subspace of L2. This Hilbert subspace contains linear transformations of elements in the domain of an integral transform, applied on functions used for computation of bounds in the Weiss-Weinstein class. The integral transform generalizes the traditional derivative and sampling operators, used for computation of existing performance lower bounds, such as the Bayesian Cram