CONVERGENCE OF MULTIPLE FOURIER-WALSH SERIES OF FUNCTIONS OF BOUNDED Λ-VARIATION

摘要

The article proves that if a summable function f(x,y) belongs to Waterman's class ΛBV([0,1]~2 ) for Λ ={ o ((n~(1/2))/(ln(n+1))~(1/2))}_(n=1)~∞ and is continuous at every point of some compact E, then the double Fourier— Walsh series of f(x, y) is uniformly u(K)—convergent on E.