Almost Everywhere Divergent Subsequences of Fourier Sums of Functions from φ(L) ∧ H1w

For a gap sequence of natural numbers {n(k)}(k=1)(infinity), for a nondecreasing function phi: [0 +infinity) -> [0, +infinity) such that phi(u) = o(u In In u) as u -> infinity, and a modulus of continuity satisfying the condition (In k)(-1) = O(w(n(k)(-1))), we present an example of a function F is an element of phi(L) boolean AND H-1(w) with an almost everywhere divergent subsequence {S-nk (F, x)} of the sequence of partial sums of the trigonometric Fourier series of the function F.