On weighted absolute convergence of multiple Fourier series of a function of (p1,…,pN)-(Λ1,…,ΛN)-BV.

We obtain a sufficient condition for the weighted β-absolute convergence of the multiple Fourier series ∑k1∈Z⋯∑kN∈Zγk1,…,kN|f^(k1,…,kN)|β,where 0<β<2 and γk1,…,kN is a weight sequence, of a function f of the class (Λ1,…,ΛN)BV(p1,…,pN)([0,2π]N). [ABSTRACT FROM AUTHOR]