Waterman classes and spherical partial sums of double Fourier series (Q1842727)

Spherical partial sums of the double trigonometric Fourier series of functions \(f\) from Waterman's class \(\Lambda\text{BV}(T^ 2)\) are investigated. It is shown that if \(f(x, y)\in \Lambda_ 0\text{BV}(T^ 2)\), where \(\Lambda_ 0= \{{1\over \sqrt n}\}^ \infty_{n= 1}\), then the spherical partial sums of its Fourier series are uniformly bounded (with respect to both \((x, y)\in T^ 2\)).