We give two-weighted norm estimates for higher order commutator of classical operators such as singular integral and fractional type operators, between weighted \(L^p\) and certain spaces that include Lipschitz, BMO and Morrey spaces. We also give the optimal parameters involved with these results, where the optimality is understood in the sense that the parameters defining the corresponding spaces belong to certain region out of which the classes of weights are satisfied by trivial weights. We also exhibit pairs of non-trivial weights in the optimal region satisfying the conditions required. Finally, we exhibit an extrapolation result that allows us to obtain boundedness results of the type described above in the variable setting and for a great variety of operators, by starting from analogous inequalities in the classical context. In order to get this result we prove a Calderón–Scott type inequality with weights that connects adequately the spaces involved.

在加权\（L ^ p \）之间，我们为经典算子（例如奇异积分和分数类型算子）的高阶交换子给出了两个加权范数估计以及某些空间，包括Lipschitz，BMO和Morrey空间。我们还给出了与这些结果有关的最佳参数，在这种意义上，从定义相应空间的参数属于某个区域的意义上理解了最佳性，在该区域中，平凡的权重可以满足权重类别。在满足所需条件的最佳区域中，我们还将展示成对的非平凡权重。最后，我们展示了一个外推结果，该结果使我们能够通过从经典语境中的不等式开始，在变量设置中获得上述类型的有界结果，并且对于各种各样的运算符。为了获得此结果，我们证明了Calderón–Scott型不等式的权重能够充分连接所涉及的空间。