Improved Hardy Inequalities with a Class of Weights

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 vector-valued function generalized vector field method. estimates show some examples this extend known case.