A Decrease in Growth of Lebesgue Constants

The Lebesgue constants of cubic partial sums of order N of n-dimensional Fourier series behave asymptotically as lnn N. For cubic linear means generated by a function vanishing only at 2n corner points the order of growth of the Lebesgue constants decreases and equals asymptotically to lnny1 N. This generalizes Kivinukk’s results where the ordinary estimates were given.