Majorant estimates for partial sums of multiple fourier series of functions from Orlicz spaces vanishing on some set

We prove relations in the braid group that generalize the relations of the formaba=bab. These relations are obtained by means of the generalization to the higher Bruhat orders of the well-known relation between the decompositions of the element of maximal length in the Weyl groupA _n−1 and some specific linear orders on the system of positive roots ofA _n−1 . Translated fromMatematicheskie Zametki, Vol. 66, No. 6, pp. 840–848, December, 1999.