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In this paper, we obtain sufficiency conditions for generalized β-absolute convergence (0  &lt;  β  ≤  2{0&lt;\beta\leq 2}   ) of single and multiple Fourier series of functions of the classΛ  -  BV   (  p   (  n  )   ↑  ∞  ,  φ  ,   [  -  π  ,  π  ]   ){\Lambda\text{-}\mathrm{BV}(p(n)\uparrow\infty,\varphi,[-\pi,\pi])}    and the class(   Λ  1   ,   Λ  2   ,  …  ,   Λ  N   )   -  BV   (  p   (  n  )   ↑  ∞  ,  φ  ,    [  -  π  ,  π  ]   N   ){(\Lambda^{1},\Lambda^{2},\dots,\Lambda^{N})\text{-}\mathrm{BV}(p(n)\uparrow% \infty,\varphi,[-\pi,\pi]^{N})}   , respectively.

Absolute convergence of multiple Fourier series of a function of p ( n )-Λ-BV