Abstract
After Alexits [6], Leindler [6, 71, and Gogoladze [ 1 ] investigated estimates of strong approximation by Fourier series in 1965, G. Freud [8] raised the corresponding saturation problem in 1969. Study on this topic has since been carried on over a decade, but it seems that most of the results obtained are limited to the case of one dimension [9-l 11. The saturation problem in two dimensions was considered in [2]. Let C*nxZn be the space of continuous functions with period 2~ in each variable. For f(x, y) E C,, x Zlr, let S,,df, x, y) denote the Fourier partial sums, and &,df> = infrmn Ilf L, llcl X2n the best uniform approximation off by double trigonometric polynom]als of order m, n. (We use I( . I] to denote ]] . l]cZnXZn henceforth.) We consider the rectangular strong approximation operator HLN defined by
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