Estimates for the norm of the error functional in the spaces $S_p$ for the weight quadrature formulas exact for Haar polynomials

The following estimates for the norm of the error functional are obtained in the spaces $S_p$: a low estimate of $\|\delta_N\|_{S_p^*}$ in the case of the quadrature formulas exact for constants and some upper estimates of $\|\delta_N\|_{S_p^*}$ in the case of the quadrature formulas possessing the Haar $d$-property.