In the framework of Hardy type inequalities and their applications to evolution problems, paper deals with local nonlocal weighted improved related study Kolmogorov operators perturbed by singular potentials. The class weights is wide enough. We focus our attention on potentials obtained inverse square adding a nonnegative correction term. method used get results based introduction suitable vec...

In this paper we obtain some new estimates for multilinear exponential sums in prime fields with a more general class of weights than previously considered. Our techniques are based on recent progress Shkredov which has roots Rudnev's point plane incidence bound. We apply our to results concerning sparse polynomials and Weyl over small generalized arithmetic progressions.