Necessary conditions of optimality of quadrature formulas with weight on some classes of differentiable functions

For the quadrature formula (with positive, continuous weight function) that is defined by the values of the function and its derivatives of up to and including $(r-1)$-th order, we find necessary conditions of optimality on the classes $W^r_p$, $r = 1, 2, \ldots$, $p = 2$, $p = \infty$.