On the order of growth of rectangular partial sums of double orthogonal series

We obtain estimates of the order of growth of rectangular partial sums of double orthogonal series and establish their unimprovability on the set of all double orthogonal systems. South-Ukrainian Pedagogical University, Odessa. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 51, No. 10, pp. 1299–1310, October. 1999.