Abstract. The convergence of Cesàro means of negative order of double trigonometric Fourier series of functions of bounded partial $\Lambda $-variation is investigated. The sufficient and neccessary conditions on the sequence $\Lambda =\{\lambda_{n}\} $ are found for the convergence of Cesàro means of Fourier series of functions of bounded partial $\Lambda $-variation.

AMS Subject Classification (1991): 42B08

Keyword(s): Fourier series, $\Lambda $-variation, generalized variation, Cesàro means

Received March 12, 2010, and in revised form May 17, 2010. (Registered under 19/2010.)